Column 1 Column 2 (i) X-rays (a) ν = 100-0 104 Hz (ii) UV (b) ν = 1010Hz (iii) Long radio waves (c) ν = 1016 Hz (iv) Microwave (d) ν = 1018Hz Column 1 Column 2 (i) X-rays (d) ν = 1018Hz (ii) UV...
Match the following
Rule Principle (i) Hund’s Rule (a) No two electrons in an atom can have the same set of four quantum numbers. (ii) Aufbau Principle (b) Half-filled and filled orbitals have extra stability....
Match the quantum numbers with the information provided by these Quantum number Information provided
Column 1 Column 2 (i) Principal quantum number (a) orientation of the orbital (ii) Azimuthal quantum number (b) energy and size of orbital (iii) Magnetic quantum number (c) spin of an electron (iv)...
Match the following species with their corresponding ground state electronic configuration.
Atom / Ion Electronic configuration (i) Cu (a) 1s2 2s2 2p6 3s2 3p6 3d10 (ii) Cu2+ (b) 1s2 2s2 2p6 3s2 3p6 (iii) Zn2+ (c) 1s2 2s2 2p6 3s2 3p6 3d10 4s1 (iv) Cr3+ (d) 1s2 2s2 2p6 3s2 3p63d9 (e) 1s2...
The hydrogen atom has only one electron, so mutual repulsion between electrons is absent. However, in multielectron atoms mutual repulsion between the electrons is significant. How does this affect the energy of an electron in the orbitals of the same principal quantum number in multielectron atoms?
Hydrogen atom has only one electron, so the mutual repulsion between the electrons is non-existent. However, in multielectron atoms the interaction between electrons is important. This is because,...
A hypothetical electromagnetic wave is shown in Figure. Find out the wavelength of the radiation.
Distance between the two identical successive points in a wave is called the wavelength. Given, In the hypothetical wave, Wavelength, λ = 4 × 2.16 pm Hence, Wavelength, λ = 8.64 pm.
Chlorine exists in two isotopic forms, Cl-37 and Cl-35 but its atomic mass is 35.5. This indicates the ratio of Cl-37 and Cl-35 is approximately
(i) 1:2 (ii) 1:1 (iii) 1:3 (iv) 3:1 Correct Answer: (iii) 1:3 Explanation: Ratio of isotope abundance of Chlorine 37 to Chlorine 35 = A1:A2 Ratio of isotope abundance of Chlorine 37...
Orbital angular momentum depends on __________.
(i) l (ii) n and l (iii) n and m (iv) m and s Correct Answer: (i) l Explanation: Orbital angular momentum depends on the value of l which is referred to as the azimuthal quantum number.
A total number of orbitals associated with the third shell will be __________.
(i) 2 (ii) 4 (iii) 9 (iv) 3 Correct Answer: (iii) 9 Explanation: The total number of orbitals in nth shell = n2 Hence, the total number of orbitals associated with the third shell will...
Which of the following is responsible to rule out the existence of definite paths or trajectories of electrons? (i) Pauli’s exclusion principle. (ii) Heisenberg’s uncertainty principle. (iii) Hund’s rule of maximum multiplicity. (iv) Aufbau principle.
Correct Answer: (ii) Heisenberg’s uncertainty principle. Explanation: The Heisenberg's uncertainty principle states that it is impossible to know the exact position and speed of an object...
The number of radial nodes for 3p orbital is __________.
(i) 3 (ii) 4 (iii) 2 (iv) 1 Correct Answer: (iv) 1 Explanation: Number of radial nodes for 3p orbital = 3−1−1 Number of radial nodes for 3p orbital = 3−2 Number of radial nodes for 3p...
Two atoms are said to be isobars if.
(i) they have the same atomic number but a different mass number. (ii) they have the same number of electrons but a different number of neutrons. (iii) they have the same number of neutrons but a...
Which of the following properties of an atom could be explained correctly by Thomson Model of an atom?
(i) Overall neutrality of atom. (ii) Spectra of a hydrogen atom. (iii) Position of electrons, protons and neutrons in an atom. (iv) Stability of atom. Correct Answer: (i) Overall...
Which of the following statements about the electron is incorrect?
(i) It is a negatively charged particle. (ii) The mass of an electron is equal to the mass of a neutron. (iii) It is a basic constituent of all atoms. (iv) It is a constituent of cathode rays....
Which of the following statement is not correct about the characteristics of cathode rays?
(i) They start from the cathode and move towards the anode. (ii) They travel in a straight line in the absence of an external electrical or magnetic field. (iii) Characteristics of cathode rays do...
The probability density plots of 1s and 2s orbitals are given in Figure:
The density of dots in a region represents the probability density of finding electrons in the region. Based on the above diagram which of the following statements is incorrect? (i) 1s and 2s...
Which of the following options does not represent ground state electronic configuration of an atom?
(i) 1s2 2s2 2p6 3s2 3p6 3d8 4s2 (ii) 1s2 2s2 2p6 3s2 3p6 3d9 4s2 (iii) 1s2 2s2 2p6 3s2 3p6 3d10 4s1 (iv) 1s2 2s2 2p6 3s2 3p6 3d5 4s1 Correct Answer: (ii) 1s2 2s2 2p6 3s2 3p6 3d9 4s2...
Which of the following conclusions could not be derived from Rutherford’s α -particle scattering experiment?
(i) Most of the space in the atom is empty. (ii) The radius of the atom is about 10–10 m while that of a nucleus is 10–15 m. (iii) Electrons move in a circular path of fixed energy called orbits....
A box contains some identical red coloured balls, labelled as A, each weighing 2 grams. Another box contains identical blue coloured balls, labelled as B, each weighing 5 grams. Consider the combinations AB, AB2, A2B and A2B3 and show that the law of multiple proportions is applicable.
AB ab2 A,B A2B3 Mass of A (in g) 2 2 4 415 Mass of B (in g) 5 10 5 According to the law of multiple proportions, Masses of B combines with a constant mass of A are 10g, 20g, 5g, 15g Simple...
Assertion (A): Combustion of 16 g of methane gives 18 g of water. Reason (R): In the combustion of methane, water is one of the products. (i) Both A and R are true but R is not the correct explanation of A. (ii) A is true but R is false. (iii) A is false but R is true. (iv) Both A and R are false.
Correct Answer: (iii) A is false but R is true Explanation: Combustion of 16 g of methane gives 36 g of water.
Assertion (A): Significant figures for 0.200 is 3 whereas for 200 it is 1. Reason (R): Zero at the end or right of a number are significantly provided they are not on the right side of the decimal point. (i) Both A and R are true and R is the correct explanation of A. (ii) Both A and R are true but R is not a correct explanation of A. (iii) A is true but R is false. (iv) Both A and R are false.
Correct Answer: (iii) A is true but R is false Explanation: Zero at the end of a number without the decimal point is not significantly based on the rate of accuracy.
The reactant which is entirely consumed in the reaction is known as limiting reagent. In the reaction 2A + 4B → 3C + 4D, when 5 moles of A react with 6 moles of B, then (i) which is the limiting reagent? (ii) calculate the amount of C formed?
(i) The reactant B is the the limiting reagent. (ii) Calculation: Let us consider that the reactant B got completely consumed as it is the limiting reagent. 4 mol of B gives 3 mol of C 6 mol of B...
The density of 3 molal solutions of NaOH is 1.110 g mL–1. Calculate the molarity of the solution.
Calculation: 3 molal solution of NaOH = 3 moles of NaOH dissolved in water 3 mole of NaOH = 120g Density of solution = 1.110gmL-1 Volume = mass/density Volume = 1120g/1.110gmL-1 Volume =1.009L...
Calculate the average atomic mass of hydrogen using the following data :
Isotope % Natural abundance Molar mass 1H 99.985 1 2H 0.015 2 Calculation: Average atomic mass of Hydrogen \[=099.985\times 1+\frac{0.015\times 2}{100}\] ...
45.4 L of dinitrogen reacted with 22.7 L of dioxygen and 45.4 L of nitrous oxide was formed. The reaction is given below:
2N2(g) + O2(g) → 2N2O(g) Which law is being obeyed in this experiment? Write the statement of the law? Answer: The Gay-Lussac’s law is used in the given reaction. The Gay-Lussac’s law states...
Which of the following terms is unitless?
(i) Molality (ii) Molarity (iii) Mole fraction (iv) Mass per cent Answer: Correct Answers: (iii) Mole fraction; (iv) Mass per cent Explanation: Unit of Molality - Molal or moles per kg Unit...
16 g of oxygen has the same number of molecules as in
(i) 16 g of CO (ii) 28 g of N2 (iii) 14 g of N2 (iv) 1.0 g of H2 Answer: Correct Answers: (iii) 14 g of N2; (iv) 1.0 g of H2 Explanation: The no. of molecules in N2 is 0.5 × 6.023 × 1023 The...
What will be the molality of the solution containing 18.25 g of HCl gas in 500 g of water? (i) 0.1 m (ii) 1 M (iii) 0.5 m (iv) 1 m
Correct Answer: (iv) 1 m Explanation: According to molality of a substance which is the number of mass of solute per mass of the solvent in liters, the molality of the solution containing 18.25 g of...
If the concentration of glucose (C6H12O6) in the blood is 0.9 g L-1, what will be the molarity of glucose in the blood? (i) 5 M (ii) 50 M (iii) 0.005 M (iv) 0.5 M
Correct Answer: (iii) 0.005 M Explanation: According to the molarity of a substance which is defined as the number of moles per volume of the solution in litres, the molarity of the glucose in blood...
The number of atoms present in one mole of an element is equal to Avogadro number. Which of the following element contains the greatest number of atoms? (i) 4g He (ii) 46g Na (iii) 0.40g Ca (iv) 12g He
Correct Answer: (iv) 12g He Explanation: The number of atoms present in 4g of Helium – 1 NA The number of atoms present in 46g of Sodium - 2 NA The number of atoms present in 0.04g of Calcium – 0.01...
If 500 mL of a 5M solution is diluted to 1500 mL, what will be the molarity of the solution obtained? (i) 1.5 M (ii) 1.66 M (iii) 0.017 M (iv) 1.59 M
Correct Answer: (ii) 1.66 M Explanation: According to the Using M1V1= M2V2 formula, the value of M2 is 1.66 M.
What will be the molarity of a solution, which contains 5.85 g of NaCl(s) per 500 mL? (i) 4 mol L-1 (ii) 20 molL-1 (iii) 0.2 molL-1 (iv) 2molL-1
Correct Answer: (iii) 0.2 molL-1 Explanation: The Molarity is defined as the number of moles per volume of the solution in litres. Given, Mass = 5.85g Molar mass = 58.5 g/mol Volume of the solution...
A measured temperature on the Fahrenheit scale is 200 °F. What will this reading be on a Celsius scale? (i) 40 °C (ii) 94 °C (iii) 93.3 °C (iv) 30 °C
Correct Answer: (iii) 93.3 °C Explanation: According to the relationship between the temperature in Fahrenheit and Celsius scale, the temperature on Celsius scale is 93.3 °C.
Two students performed the same experiment separately and each one of them recorded two readings of mass which are given below. The correct reading of mass is 3.0 g. Based on given data, mark the correct option out of the following statements. Student Readings
(i) (ii) A 3.01 2.99 B 3.05 2.95 (i) Results of both the students are neither accurate nor precise. (ii) Results of student A are both precise and accurate. (iii) Results of student B are neither...
Separation of Motion of a system of particles into motion of the centre of mass and motion about the centre of mass:
(i) Show where is the angular momentum of the system about the centre of mass with velocities considered with respect to the centre of mass. Note , rest of the notation is the standard notation used in the lesson. Note L’ and MR can be said to be angular momenta, respectively, about and of the centre of mass of the system of particles.
(ii) Prove that : Further prove that: Where t’ext is the sum of all external torques acting on the system about the centre of mass. (Clue : A pply Newton’s Third Law and the definition of centre of mass. Consider that internal forces between any two particles act along the line connecting the particles.)
Here $\vec{r}_{i}=\vec{r}_{i}+\vec{R}+R \ldots$ (1) also, $\vec{V}_{i}=\vec{V}_{i}+\vec{V} \ldots \ldots .$ (2) Where $\vec{r}_{i}^{\overrightarrow{3}}$ and $\vec{v}_{i}^{\overrightarrow{3}}$ denote...
Separation of Motion of a system of particles into motion of the centre of mass and motion about the centre of mass:
Show Where is the momentum of the particle (of mass and Note is the velocity of the particle with respect to the centre of mass.Also, verify using the definition of the centre of mass that
(ii) Prove that Where is the total kinetic energy of the system of particles, is the total kinetic energy of the system when the particle velocities are taken relative to the center of mass and is the kinetic energy of the translation of the system as a whole.
i)Here $\vec{r}_{i}=\vec{r}_{i}+\vec{R}+R \ldots$ also, $\vec{V}_{i}=\vec{V}_{i}+\vec{V} \ldots \ldots .$ Where $\vec{r}_{i}^{\overrightarrow{3}}$ and $\vec{v}_{i}^{\overrightarrow{3}}$ denote the...
Read the statement below carefully, and state, with reasons, if it is true or false; A wheel moving down a perfectly frictionless inclined plane will undergo slipping (not rolling) motion.
True. Rolling happens only when there is a frictional force to provide the torque; otherwise, the wheel merely slips down the plane on its own weight.
Read each statement below carefully, and state, with reasons, if it is true or false;
(a) The instantaneous acceleration of the point of contact during rolling is zero.
(b) For perfect rolling motion, work done against friction is zero.
(a) False. The instantaneous acceleration of a rolling object will have a value that is not zero. (b) True. Because the frictional force is zero during perfect rolling, no work is done against it.
Read each statement below carefully, and state, with reasons, if it is true or false;
(a) During rolling, the force of friction acts in the same direction as the direction of motion of the CM of the body.
(b) The instantaneous speed of the point of contact during rolling is zero.
(a) False. The direction of frictional force is the polar opposite of the centre of mass's motion. Because the centre of mass of a rolling object moves backwards, the frictional force acts in the...
A cylinder of mass and radius is rolling perfectly on a plane of inclination The coefficient of static friction . If the inclination of the plane is increased, at what value of does the cylinder begin to skid, and not roll perfectly?
The given situation can be depicted as: Mass is given as $m=10 \mathrm{~kg}$ Radius is given as $r=15 \mathrm{~cm}=0.15 \mathrm{~m}$ Co-efficient of kinetic friction is given as $\mu_{s}=0.25$ Angle...
A cylinder of mass and radius is rolling perfectly on a plane of inclination The coefficient of static friction
(a) How much is the force of friction acting on the cylinder?
(b) What is the work done against friction during rolling?
The above situation can be depicted as: Mass is given as $m=10 \mathrm{~kg}$ Radius is given as $r=15 \mathrm{~cm}=0.15 \mathrm{~m}$ Co-efficient of kinetic friction is given as $\mu_{s}=0.25$ Angle...
A solid disc and a ring, both of radius are placed on a horizontal table simultaneously, with an initial angular speed equal to . Which of the two will start to roll earlier? The coefficient of kinetic friction is
The radius of the ring and the disc is given as r = 10 cm = 0.10 m Initial angular speed is given as ω0 =10 π rad s–1 The coefficient of kinetic friction is given as μk = 0.2 According to Newton’s...
A disc rotating about its axis with angular speed is placed lightly (without any translational push) on a perfectly frictionless table. The radius of the disc is R. What are the linear velocities of the points and on the disc shown in Figure. Will the disc roll in the direction indicated?
Solution: The respective linear velocities are : For point $A, v_{A}=r \omega_{0}$ For point $B, v_{B}=r \omega_{0}$ both in the direction of arrow For point $C, v_{c}=(R / 2) \omega_{0}$ in the...
Prove the result that the velocity v of translation of a rolling body (like a ring, disc, cylinder or sphere) at the bottom of an inclined plane of a height is given by using dynamical consideration (i.e. by consideration of forces and torques). Note is the radius of gyration of the body about its symmetry axis, and is the radius of the body. The body starts from rest at the top of the plane.
The given question can be represented as: where, $R$ is the body's radius $g$ is the acceleration due to gravity $\mathrm{K}$ is the body's radius of gyration $v$ is the body's translational...
(a) Prove the theorem of perpendicular axes. (Hint: Square of the distance of a point in the plane from an axis through the origin and perpendicular to the plane is .
(b) Prove the theorem of parallel axes. (Hint: If the centre of mass of a system of n particles is chosen to be the origin .
(a) The moment of inertia of a planar body (lamina) about an axis perpendicular to its plane is equal to the sum of the moments of inertia of the lamina about any two mutually perpendicular axes in...
Two discs of moments of inertia and about their respective axes (normal to the disc and passing through the centre), and rotating with angular speeds and are brought into contact face to face with their axes of rotation coincident.
(a) What is the angular speed of the two-disc system?
(b) Show that the kinetic energy of the combined system is less than the sum of the initial kinetic energies of the two discs. How do you account for this loss in energy? Take
(a) Let I1 and I2 be the moment of inertia of the two turntables respectively. Let ω1 and ω2 be the angular speed of the two turntables respectively. So, we can say, Angular momentum of turntable...
A bullet of mass and speed is fired into a door and gets embedded exactly at the centre of the door. The door is wide and weighs . It is hinged at one end and rotates about a vertical axis practically without friction. Find the angular speed of the door just after the bullet embeds into it.
Velocity is given as v = 500 m/s Mass of bullet is given as m = 10 g or 10 × 10–3 kg The width of the door is given as L = 1 m The radius of the door is given as r = 1 / 2 Mass of the door is given...
A man stands on a rotating platform, with his arms stretched horizontally holding a weight in each hand. The angular speed of the platform is 30 revolutions per minute. The man then brings his arms close to his body with the distance of each weight from the axis changing from to . The moment of inertia of the man together with the platform may be taken to be constant and equal to .
(a) What is his new angular speed? (Neglect friction.)
(b) Is kinetic energy conserved in the process? If not, from where does the change come about?
Mass of each weight is given as 5 kg The moment of inertia of the man-platform system is given as 7.6 kg m2 So, the moment of inertia when his arms are fully stretched to 90 cm can be calculated as,...
As shown in Figure the two sides of a step ladder BA and CA are long and hinged at A. A rope DE, m is tied halfway up. A weight is suspended from a point F, from B along with the ladder BA. Assuming the floor to be frictionless and neglecting the weight of the ladder, find the tension in the rope and forces exerted by the floor on the ladder. (Take ) (Hint: Consider the equilibrium of each side of the ladder separately.)
Solution: The above figure can be redrawn as, where, $N_{B}$ is the force being applied by floor point $B$ on the ladder $N_{c}$ is the force being applied by floor point $C$ on the ladder The...
1.0 mol of a monoatomic ideal gas is extended from the state (1) to state (2) as displayed in Fig. 6.4. Ascertain the turn out accomplished for the development of gas from the state (1) to state (2) at 298 K.
solution: \[\begin{array}{*{35}{l}} W=\text{ }\text{ }2.303nRT\text{ }log\text{ }\left( p1/p2 \right) \\ ~ \\ =\text{ }\text{ }2.303\text{ }\times \text{ }1\text{ }mol\text{ }\times \text{...
Enthalpy graph for a specific response is given in Fig. Is it conceivable to choose the immediacy of a response from the given chart? Clarify.
solution: From the given enthalpy outline it tends to be said the adjustment of enthalpy ∆H is positive for the response, for example it will be endothermic. In any case, when goes to the suddenness...
Address the likely energy/enthalpy change in the accompanying cycles graphically. (a) Throwing a stone starting from the earliest stage rooftop.
In which of the cycles likely energy/enthalpy change is contributing variable to the immediacy?
solution: Among these two cycles, simultaneously or response (b) the expected energy/enthalpy change is contributing component to the immediacy.
How might you ascertain work done on an optimal gas in a pressure, when an adjustment of tension is completed in boundless advances?
solution: At the point when an optimal gas in a pressure, where the adjustment of tension is completed in boundless advances for example through a reversible interaction, the work done can be...
ideal gas encased in a chamber, when it is compacted by steady outer strain, pext in a solitary advance as displayed in Fig? Clarify graphically.
solution: From this chart we can get the be the work done on the ideal gas encased in the chamber in 1 stage: the region covered by P-V diagram (concealed locale) is the real worth of the...
A solid cylinder rolls up an inclined plane of the angle of inclination At the bottom of the inclined plane, the centre of mass of the cylinder has a speed of .
(a) How far will the cylinder go up the plane?
(b) How long will it take to return to the bottom?
initial velocity of the solid cylinder is given $v=5 \mathrm{~m} / \mathrm{s}$ Angle of inclination is given as $\theta=30^{\circ}$ We assume that the cylinder goes up to a height of $h$, so we get:...
The oxygen molecule has a mass of and a moment of inertia of about an axis through its centre perpendicular to the lines joining the two atoms. Suppose the mean speed of such a molecule in a gas is and that its kinetic energy of rotation is two-thirds of its kinetic energy of translation. Find the average angular velocity of the molecule.
Mass of one oxygen molecule is given as $m=5.30\times10^{-26}kg$ So, the mass of each oxygen atom will be $\frac{m}{2}$ Moment of inertia is given as $I=1.94\times10^{-46}kg m^{2}$ Velocity of the...
A hoop of radius weighs . It rolls along a horizontal floor so that its centre of mass has a speed of How much work has to be done to stop it?
Radius of the ring is given as $r=2 \mathrm{~m}$ Mass of the ring s given as $m=100 \mathrm{~kg}$ Velocity of the hoop is given as $v=20 \mathrm{~cm} / \mathrm{s}=0.2 \mathrm{~m} / \mathrm{s}$ Total...
A solid sphere rolls down two different inclined planes of the same heights but different angles of inclination. (a) Will it reach the bottom with the same speed in each case? (b) Will it take longer to roll down one plane than the other? (c) If so, which one and why?
(a) Let m be the mass of the ball let h be the height of the ball let v be the final velocity of the ball at the bottom of the plane The ball possesses Potential energy $mgh$ at the top of the...
An example of 1.0 mol of a monoatomic ideal gas is taken through a cyclic interaction of extension and pressure as displayed in Fig. What will be the worth of ∆H for the cycle in general?
solution: In the accompanying cyclic ( 1 → 2 →3 →1 ) measure the underlying and last point is something very similar (for example 1). Subsequently the enthalpy change or\[H=\text{ }0\]...
The strain volume work for an ideal gas can be determined by utilizing the articulation w= ʃPexdv. The work can likewise be determined from the pV–a plot by utilizing the region under the bend inside as far as possible. At the point when an ideal gas is compacted (a) reversibly or (b) irreversibly from volume Vi to Vf. pick the right alternative.
Arrangement: Alternative (ii) is the appropriate response. w (reversible) < w (irreversible) Region under the bend is more noteworthy in irreversible pressure than that of reversible...
An ideal gas is permitted to grow against a consistent strain of 2 bar from 10 L to 50 L in one stage. Compute the measure of work done by the gas. In the event that a similar development were done reversibly, will the work is done be higher or lower than the prior case?
solution: \[\begin{array}{*{35}{l}} Measure\text{ }of\text{ }work\text{ }done\text{ }=\text{ }-\text{ }pext\text{ }V \\ ~ \\ =\text{ }\text{ }2\text{ }bar\text{ }\times \text{ }\left(...
The enthalpy of response for the response :
What will be standard enthalpy of development of H2O (l)?
solution: For the given response : \[2H2\left( g \right)\text{ }+\text{ }O2\left( g \right)\text{ }\to 2H2O\left( l \right)\] the standard enthalpy of response is \[Hr\Theta \text{ }=\text{...
The enthalpy of vapourisation of CCl4 is 30.5 kJ mol–1. Compute the warmth needed for the vapourisation of 284 g of CCl4 at steady tension.
solution: The enthalpy of vapourisation is given \[\begin{array}{*{35}{l}} for\text{ }1\text{ }mole\text{ }of\text{ }CCl4\text{ }=\text{ }30.5\text{ }kJ\text{ }mol1 \\ ~ \\...
The net enthalpy change of a response is the measure of energy needed to break every one of the bonds in reactant atoms less the measure of energy needed to shape every one of the bonds in the item particles. What will be the enthalpy change for the accompanying response?
Considering that Bond energy of H2, Br2 and HBr is 435 kJ mol–1, 192 kJ mol–1 and 368 kJ mol–1 separately.
solution: For the response \[H2\left( g \right)\text{ }+\text{ }Br2\left( g \right)\text{ }\to 2HBr\left( g \right)\] \[\begin{array}{*{35}{l}} Enthalpy\text{ }change \\ ~ \\ =\text{...
On the off chance that the burning of 1g of graphite produces 20.7 kJ of warmth, what will be molar enthalpy change? Offer the meaning of the hint too.
solution: The warmth of ignition ∆Hc of graphite (for example carbon) is given as \[=\text{ }20.7\text{ }kJ\] for 1g of graphite (C). \[1\text{ }mole\text{ }of\text{ }Carbon\text{...
The contrast among CP and CV can be inferred utilizing the experimental connection
. Work out the distinction among CP and CV for 10 moles of an optimal gas.
solution: For an optimal gas, the distinction between these two \[is\text{ }CP\text{ }\text{ }CV\text{ }=\text{ }nR,\] the all inclusive gas consistent and \[where\text{ }n=\text{ }no.\text{...
Warmth limit (Cp) is a broad property yet explicit warmth (c) is an escalated property. What will be the connection between Cpand c for 1 mol of water?
solution: \[\begin{array}{*{35}{l}} For\text{ }water,\text{ }molar\text{ }warmth\text{ }limit\text{ }=\text{ }18\text{ }x\text{ }Specific\text{ }warmth\text{ }or \\ ~ \\ Cp~=\text{...
Development of gas in a vacuum is called free extension. Ascertain the work is done and the adjustment of inner energy when 1 liter of an ideal gas grows isothermally into a vacuum until its complete volume is 5 liter?
solution: Work done in vacuum is determined by : \[\begin{array}{*{35}{l}} -\text{ }w\text{ }=\text{ }Text\text{ }\left( Vinitial\text{ }\text{ }Vfinal\text{ } \right) \\ ~ \\...
Despite the fact that warmth is a way work yet warms consumed by the framework under certain particular conditions is free of way. What are those conditions? Clarify.
solution: Warmth is free of the way under 2 conditions: At the point when the volume of the framework is kept steady By first law of thermodynamics: ...
Foresee the adjustment of inward energy for a secluded framework at steady volume.
solution: For a disengaged framework \[q=0\text{ }and\text{ }w=0\] What's more, as indicated by first law of thermodynamics: \[U=\text{ }q\text{ }+\text{ }w\text{ }\left(...
Explain why (d) A fluid flowing out of a small hole in a vessel results in a backward thrust on the vessel (e) A spinning cricket ball in air does not follow a parabolic trajectory
Answer : (d) This is due to the conservation of momentum principle. The vessel gains backward motion while the flowing fluid gains forward momentum. (e) If there had been no air, a spinning cricket...
Explain why (c) The size of the needle of a syringe controls flow rate better than the thumb pressure exerted by a doctor while administering an injection
Answer : (c) The needle size determines the flow velocity, while thumb pressure determines the pressure. Bernoulli's theorem states that P + 1/2pv2 = constant. The pressure P has a single power in...
Which amount out of ΔrG and ΔrGΘwill be zero at harmony?
solution: Gibbs energy for a response in which all reactants and items are in standard state. ΔrG° is identified with the harmony consistent of the response as follows ...
Explain why (a) To keep a piece of paper horizontal, you should blow over, not under, it (b) When we try to close a water tap with our fingers, fast jets of water gush through the openings between our fingers
Answer : (a) When we blow over a piece of paper, the velocity of the air above it becomes greater than the velocity of the air below it. According to Bernoulli's theorem, as the K.E. of air above...
The molar enthalpy of vapourisation of CH3)2CO is not exactly that of water. Why?
solution: Water has solid hydrogen bonds and the high extremity likewise accumulates in coming about it to bubble at higher temperatures. Thus water has a higher molar enthalpy than CH3)2CO....
Distinguish the state capacities and way works out of the accompanying : enthalpy, entropy, heat, temperature, work, free energy.
solution: State capacities: enthalpy, entropy, temperature and free energy. Way works: Heat and work
Fill in the blanks using the word(s) from the list appended with each statement:
(c) For solids with an elastic modulus of rigidity, the shearing force is proportional to … , while for fluids, it is proportional to … (shear strain/rate of shear strain) (d) For a fluid in a...
Fill in the blanks using the word(s) from the list appended with each statement: (a) The surface tension of liquids generally … with temperatures (increases/decreases) (b) The viscosity of gases … with temperature, whereas the viscosity of liquids … with temperature (increases/decreases)
Answer : (a) Decreases (b) increases; decreases
The standard molar entropy of H2O (l ) is 70 J K–1 mol–1. Will the standard molar entropy of H2O(s) be more, or under 70 J K–1 mol–1?
solution: The standard molar entropy of H20 (1) is 70 J K-1 mol-1. The strong type of H20 is ice. In ice, atoms of H20 are less irregular than in fluid water. In this way, molar entropy of...
Explain why (c) Surface tension of a liquid is independent of the area of the surface (d) Water with detergent disolved in it should have small angles of contact. (e) A drop of liquid under no external forces is always spherical in shape
Answer : (c) Because of surface tension, a liquid will always try to obtain the smallest possible surface area. A liquid drop will always take the shape of a sphere under zero external pressures...
Explain why (a) The angle of contact of mercury with glass is obtuse, while that of water with glass is acute. (b) Water on a clean glass surface tends to spread out while mercury on the same surface tends to form drops. (Put differently, water wets glass while mercury does not.)
Answer : (a) Water molecules exhibit weak intermolecular interactions but are attracted to solids by a strong force. As a result, they flow out. Mercury molecules, on the other hand, have a stronger...
A cyclist is riding with a speed of 27 km/h. As he approaches a circular turn on the road of a radius of 80 m, he applies brakes and reduces his speed at the constant rate of 0.50 m/s every second. What is the magnitude and direction of the net acceleration of the cyclist on the circular turn?
Answer : According to the question, the speed of the cyclist is 27 km/h Or, 27 x (5/18) = 7.5 m/s And radius of the road is 80 m The braking and the centripetal acceleration cause the net...
A fighter plane flying horizontally at an altitude of 1.5 km with a speed of 720 km/h passes directly overhead an anti-aircraft gun. At what angle from the vertical should the gun be fired for the shell with muzzle speed 600 m s-1 to hit the plane? At what minimum altitude should the pilot fly the plane to avoid being hit? (Take g = 10 m s-2 ).
Answer : According to the question, speed of the fighter plane is 720 km/h or, 720 x (5/18) = 200 m/s Altitude of the plane is1.5 km and the velocity of the shell is 600 m/s From the diagram above,...
As warm harmony complies with the zeroth law of thermodynamics, temperature of framework and environmental elements will be a similar when they are in warm balance.
solution: For the given response \[N2O4\text{ }\left( g \right)\leftrightharpoons 2NO2\text{ }\left( g \right)\text{ }the\text{ }worth\text{ }of\text{ }Kp\text{ }=\text{ }0.98.\]...
Expansion in enthalpy of the environmental elements is equivalent to the lessening in enthalpy of the framework. Will the temperature of the framework and environmental elements be a similar when they are in warm balance?
solution: As warm balance submits to the zeroth law of thermodynamics, temperature of framework and environmental factors will be a similar when they are in warm balance.
The warmth affects a framework and temperature is the proportion of normal tumultuous movement of particles in the framework. Compose the numerical connection which relates these three boundaries.
solution: The numerical connection which relates these three boundaries is \[\Delta S\text{ }=\text{ }qrev/T\] where ΔS is the adjustment of entropy and T represents...
A bullet fired at an angle of 30° with the horizontal hits the ground 3.0 km away. By adjusting its angle of projection, can one hope to hit a target 5.0 km away? Assume the muzzle speed to be fixed, and neglect air resistance.
Ans: According to the question, the bullet is fired at an angle of 30° And the bullet impacts the ground at a distance = 3km or 3000 m Exprsssion for the Horizontal range is : R = u2 sin2θ/g Upon...
The position of a particle is given by
\[r=3.0t\hat{i}-2.0{{t}^{2}}\hat{j}+4.0\hat{k}m\] Where t is in seconds and the coefficients have the proper units for r to be in meters. (a) Find the ‘v’ and ‘a’ of the particle? (b) What is the...
. Utilize the accompanying information to ascertain Δlattice Hθfor NaBr.
solution: Sublimation of the metal(ΔsubHΘ) →Ionization of the metal (ΔiHΘ) →Dissociation of the non-metal (ΔdissHΘ) →Gain of electrons by the non-metal(ΔegHΘ) \[\Delta f\text{ }H\theta...
The enthalpy of atomisation for the response
. What is the bond energy of the C–H bond?
solution: For 1 C-H bond, the bond energy will be equivalent to 1/4 that of the enthalpy of atomisation \[=\text{ }\left( 1665/4 \right)\text{ }=\text{ }416.25\text{ }kJ\text{...
. Enthalpy is a broad property. As a rule, if the enthalpy of a general response A→B along one course is Δr H and Δr H1, ΔrH2, ΔrH3 … .. address enthalpies of middle responses prompting item B. What will be the connection between ΔrH for generally speaking response and ΔrH1, ΔrH2… .. and so forth for moderate responses.
solution: For the response, A→B the development of B goes through a few middle of the road responses with various enthalpy esteems Δr H1, ΔrH2, ΔrH3… .., and the general enthalpy change is Δr...
. The worth of
. Compute the enthalpy change for the accompanying response :
solution: Enthalpy change of a response is determined as : Σbond enthalpy of reactants-Σbond enthalpy of items for the deterioration \[\begin{array}{*{35}{l}} 2NH3\left( g...
Standard molar enthalpy of arrangement, Δf Hθis simply a unique instance of enthalpy of response, Δr Hθ. Is the Δr Hθfor the accompanying response same as Δf Hθ? Offer the justification behind your response.
solution: The given response \[CaO\left( s \right)\text{ }+\text{ }CO2\left( g \right)\text{ }\to CaCO3\left( s \right)\] is demonstrating that it is happening in the standard type of 1 mole...
. One mole of CH3)2CO requires less warmth to disintegrate than 1 mol of water. Which of the two fluids has a higher enthalpy of vapourisation?
solution: Among the two fluids, water has a higher enthalpy of vapourisation (burning-through higher warmth energy). Thusly, ∆Hvapourisation (water) > ∆Hvapourisation...
18.0 g of water totally vapourises at 100°C and 1 bar pressure and the enthalpy change in the process is 40.79 kJ mol–1. What will be the enthalpy change for vapourising two moles of water under similar conditions? What is the standard enthalpy of vapourisation for water?
solution: Enthalpy change of vapourisation for \[1\text{ }mole\text{ }=\text{ }40.79\text{ }kJ\text{ }mol1\] enthalpy change of vapourisation for \[2\text{ }moles\text{ }of\text{ }water\text{...
. Think about the accompanying response among zinc and oxygen and pick the right alternatives out of the choices given underneath :
(i) The enthalpy of two moles of ZnO is not exactly the absolute enthalpy of two moles of Zn and one mole of oxygen by 693.8 kJ. (ii) The enthalpy of two moles of ZnO is more than the absolute enthalpy of two moles of Zn and one mole of oxygen by 693.8 kJ. (iii) 693.8 kJ mol–1 energy is advanced in the response. (iv) 693.8 kJ mol–1 energy is caught up in the response.
solution: Choice (I) and (iii) are the appropriate responses
. For an optimal gas, crafted by reversible extension under isothermal condition can be determined by utilizing the articulation
An example containing 1.0 mol of an ideal gas is extended isothermally and reversibly to multiple times of its unique volume, in two separate tests. The extension is completed at 300 K and 600 K separately. Pick the right alternative. (I) Work done at 600 K is multiple times the work done at 300 K. (ii) Work done at 300 K is double the work done at 600 K. (iii) Work done at 600 K is double the work done at 300 K. (iv) ∆U = 0 in the two cases.
solution: Alternative (iii) and (iv) are the appropriate responses. work done at 600 K is double the work done at 300 K. Since each case includes isothermal extension of an optimal gas, there...
The immediacy implies, having the capacity to continue without the help of an outer organization. The cycles which happen immediately are (I) stream of warmth from colder to hotter body. (ii) gas in a compartment contracting into one corner. (iii) gas extending to fill the accessible volume. (iv) consuming carbon in oxygen to give carbon dioxide.
solution: Alternative (iii) and (iv) are the appropriate responses. Gas grows or diffuses in accessible space suddenly, e.g., spillage of cooking gas gives smell of ethyl mercaptan...
In an exothermic response, heat is advanced, and the framework loses warmth to the encompassing. For such a framework (I) qp will be negative (ii) ∆rH will be negative (iii) qp will be positive (iv) ∆rH will be positive
solution: Choice (I) and (ii) are the appropriate responses. For an exothermic response\[,\text{ }qp~=\text{ }-\text{ }ve,\text{ }\gamma H\text{ }=\text{ }-\text{ }ve\]
. Thermodynamics essentially manages (I) interrelation of different types of energy and their change from one structure to another. (ii) energy changes in the cycles which rely just upon starting and last conditions of the minute frameworks containing a couple of particles. (iii) how and at what rate these energy changes are done. (iv) the framework in harmony state or moving from one balance state to another harmony state.
solution: Alternative (I) and (iv) are the appropriate responses. Thermodynamics manages interrelation of different types of energy and their change into one another. It additionally manages...
. Which of coming up next isn’t right? (I) ∆G is zero for a reversible response (ii) ∆G is positive for an unconstrained response (iii) ∆G is negative for an unconstrained response (iv) ∆G is positive for a non-unconstrained response
solution: Alternative (ii) is the appropriate response. ∆G gives a basis for suddenness at consistent strain and temperature. (I) If ∆G is negative (< 0). the cycle is...
. Enthalpy of sublimation of a substance is equivalent to (I) enthalpy of combination + enthalpy of vapourisation (ii) enthalpy of combination (iii) enthalpy of vapourisation (iv) double the enthalpy of vapourisation
solution: Choice (I) is the appropriate response. Enthalpy of sublimation of a substance is equivalent to enthalpy of combination + enthalpy of vapourisation. Sublimation is immediate...
The enthalpies of components in their standard states are taken as nothing. The enthalpy of arrangement of a compound (I) is consistently negative (ii) is consistently sure (iii) possibly certain or negative (iv) is rarely negative
solution: Choice (iii) is the appropriate response. Warmth of arrangement of a compound might be positive or negative.
. Consider the responses given beneath. Based on these responses discover which of the arithmetical relations given in choices (I) to (iv) is right?
solution: Choice (iii) is the appropriate response. x > y because same bonds are formed in reactions (i) and (ii) but bonds between reactant molecules are broken only in reaction...
Based on thermochemical conditions (a), (b) and (c), discover which of the logarithmic connections given in alternatives (I) to (iv) is right.
solution: Choice (iii) is the appropriate response. \[\begin{array}{*{35}{l}} \left( a \right)\text{ }C\text{ }\left( graphite \right)\text{ }+\text{ }O2\text{ }\left( g \right)\text{ }\to...
The entropy change can be determined by utilizing the articulation
At the point when water freezes in a glass container, pick the right assertion among the accompanying : (I) ∆S (framework) diminishes however ∆S (environmental factors) stays as before. (ii) ∆S (framework) increments yet ∆S (environmental elements) diminishes. (iii) ∆S (framework) diminishes yet ∆S (environmental elements) increments. (iv) ∆S (framework) diminishes and ∆S (environmental factors) likewise diminishes.
solution: Alternative (iii) is the appropriate response. During the method involved with freezing energy is released,which is consumed by the environmental factors. Therefore,the entropy off...
Hydrogen bonds are formed in many compounds e.g., H2O, HF, NH3. The boiling point of such compounds depends to a large extent on the strength of hydrogen bond and the number of hydrogen bonds. The correct decreasing order of the boiling points of the above compounds is : (i) HF > H2O > NH3 (ii) H2O > HF > NH3 (iii) NH3 > HF > H2O (iv) NH3 > H2O > HF
Solution: Option (ii) is the answer.
The types of hybrid orbitals of nitrogen in NO2+, NO3- and NH4+respectively are expected to be
(i) sp, sp3 and sp2
(ii) sp, sp2 and sp3
(iii) sp2, sp and sp3
(iv) sp2, sp3 and sp
Solution: Option (ii) is the answer. The hybridisation of each molecule gives us an idea about the hybrid orbitals.
In an adiabatic interaction, no exchange of warmth happens among framework and environmental elements. Pick the right choice with the expectation of complimentary extension of an optimal gas under adiabatic condition from the accompanying.
solution: Choice (iii) is the appropriate response. With the expectation of complimentary extension w = 0 For adiabatic cycle q = 0 From first law of thermodynamics, ...
. ∆fUᶱ of arrangement of CH4 (g) at certain temperature is – 393 kJ mol–1. The worth of ∆ fHᶱ is (I) zero (ii) < ∆f Uᶱ (iii) > ∆f Uᶱ (iv) equivalent to ∆f Uᶱ
solution: Choice (ii) is the appropriate response.
During complete burning of one mole of butane, 2658 kJ of warmth is delivered. The thermochemical response for above change is
solution: Choice (iii) is the appropriate response. Exothermic reaction for combustion of one mole of butane is represented as \[\left( iii \right)\text{ }C4H10\left( g \right)\text{...
. The volume of gas is decreased to half from its unique volume. The particular warmth will be ______. (I) decrease to half (ii) be multiplied (iii) stay consistent (iv) increment multiple times
solution: Alternative (iii) is the appropriate response. The particular warmth of a substance is the warmth needed to raise the temperature of 1 gram of a substance by one degree (1 K or 1...
The condition of a gas can be portrayed by citing the relationship between___. (I) pressure, volume, temperature (ii) temperature, sum, pressure (iii) the sum, volume, temperature (iv) pressure, volume, temperature, sum
solution: Alternative (iv) is the appropriate response. Condition of a framework can be portrayed by state capacities or state factors which are pressure, volume, temperature and measure of...
Which of the accompanying assertions is right? (I) The presence of responding species in a covered measuring utencil is an illustration of an open framework. (ii) There is a trade of energy just as a matter between the framework also, the environmental elements in a shut framework. (iii) The presence of reactants in a shut vessel made down of copper is an illustration of a shut framework. (iv) The presence of reactants in a canteen jar or some other shut protected vessel is an illustration of a shut framework.
solution: Alternative (iii) is the appropriate response. For a shut vessel made down of copper, regardless of can be traded between the framework and the environmental elements however energy trade...
An aircraft is flying at a height of 3400 m above the ground. If the angle subtended at a ground observation point by the aircraft positions 10.0 s apart is 30°, what is the speed of the aircraft?
Answer : According to the question, the aircraft is flying at a height = 3400 m Let A and B represent the positions of aircraft which make an angle ∠AOB = 300. OC is a perpendicular drawn on AB. OC...
Can we associate a vector with (i) a sphere (ii) the length of a wire bent into a loop (iii) a plane area Clarify for the same.
Answer - No, No, Yes (i) We can't identify a sphere's volume with a vector, but we can associate a sphere's area with an area vector. (ii) A vector cannot be associated with the length of a wire...
As a vector is having both direction and magnitude, then is it necessary that if anything is having direction and magnitude it is termed as a vector? The rotation of an object is defined by the angle of rotation about the axis and the direction of rotation of the axis. Will it be a rotation of a vector?
Answer - No and no A physical quantity that has both direction and magnitude is not always referred to as a vector. The current, for example, is a scalar quantity despite having direction and...
Does a vector have a location in space? Will it fluctuate with time? Can two equivalent vectors x and y at various locations in space fundamentally have indistinguishable physical effects? Give cases in support of your answer.
Ans: No, Yes and No. In space, a vector has no defined place. The reason for this is that when a vector displaces in such a way that its direction and magnitude do not change, it remains invariant....
Read each statement below carefully and state, with reasons and examples, if it is true or false: A scalar quantity is one that (a) is conserved in a process (b) can never take negative values (c) must be dimensionless
Answer : (a) False Energy is not preserved in inelastic collisions, despite being a scalar quantity. b) False The temperature, although being a scalar quantity, can have negative values. c) False...
An aircraft executes a horizontal loop of radius 1 km with a steady speed of 900 km h-1.Compare its centripetal acceleration with the acceleration due to gravity.
Answer : According to the question, radius of the loop r is1 km, or 1000 m And the speed, v is 900 km h-1 = 900 ×(5/18) = 250 ms-1 Expression for centripetal accelertaion is : $...
Read each statement below carefully and state, with reasons, if it is true or false: (c) The acceleration vector of a particle in uniform circular motion averaged over one cycle is a null vector.
Answer : (c) True The direction of the acceleration vector in a uniform circular motion (UCM) is toward the circle's centre. It does, however, vary over time. A null vector is the average of these...
Read each statement below carefully and state, with reasons, if it is true or false: (a) The net acceleration of a particle in a circular motion is always along the radius of the circle towards the centre. (b) The velocity vector of a particle at a point is always along the tangent to the path of the particle at that point.
Answer : (a) False Only in the situation of uniform circular motion is the net acceleration of a particle in a circular motion directed along the radius of the circle toward the center. (b) True...
A stone tied to the end of a string 80 cm long is whirled in a horizontal circle with a constant speed. If the stone makes 14 revolutions in 25 s, what is the direction and magnitude of the acceleration of the stone?
Answer - According to the question, the length of the string, l is 80 cm, or 0.8 m and the number of revolutions is 14 And the time taken = 25 s Expression for the frequency is given as follows -...
A cricketer can throw a ball to a maximum horizontal distance of 100 m. How much high above the ground can the cricketer throw the same ball?
answer - We are given that the maximum horizontal distance is R = 100 m When the angle of projection is 45 degrees, only then the cricketer can toss the ball the maximum horizontal distance....
The ceiling of a long hall is 25 m high. What is the maximum horizontal distance that a ball is thrown with a speed of 40 ms^{-1}ms −1 can go without hitting the ceiling of the hall?
Answer : According to the question, the speed of the ball is u = 40 ms-1 And the maximum height is h = 25 m The maximum height obtained by a body projected at an angle θ in projectile motion is...
In a harbour, the wind is blowing at the speed of 72 km/h and the flag on the mast of a boat anchored in the harbour flutters along the N-E direction. If the boat starts moving at a speed of 51 km/h to the north, what is the direction of the flag on the mast of the boat?
Answer - According to the question, the velocity of the boat is 51 km/h and the velocity of the wind is 72 km/h. The flag is flapping in the direction of northeast. It indicates that the wind is...
A man can swim with a speed of 4 km/h in still water. How long does he take to cross a river 1 km wide if the river flows steadily at 3 km/h and he makes his strokes normal to the river current? How far down the river does he go when he reaches the other bank?
Answer : According to the question, speed of the man is ${{v}_{m}}=4km/h$ and the width of the river is 1 km Then the time taken in crossing the river can be determined as follows :...
Rain is falling vertically with a speed of 30 m s^{-1} . A woman rides a bicycle with a speed of 10 m s^{-1}ms −1 in the north to south direction. What is the direction in which she should hold her umbrella?
Answer : Here, vc denotes theVelocity of the cyclist = 10 m/s vr denotes the Velocity of falling rain = 30 m/s The woman must hold her umbrella in the direction of the relative velocity (v) of the...
A passenger arriving in a new town wants to go from the station to a hotel located 10 km away on a straight road from the station. A dishonest cabman takes him along a circuitous path 23 km long and reaches the hotel in 28 min. (a) What is the average speed of the taxi? (b) What is the magnitude of average velocity? Are the two equal?
Answer : (a) According to the question, the total distance travelled is 23 km and the total time taken is 28 minutes. Time Taken (in hours) = 28/60 h Average speed is given as follows : Average...
On an open ground, a motorist follows a track that turns to his left by an angle of 600 after every 500 m. Starting from a given turn, specify the displacement of the motorist at the third, sixth and eighth turn. Compare the magnitude of the displacement with the total path length covered by the motorist in each case
Answer - As shown in the diagram, the motorist's path is a regular hexagon with a 500-meter side. Let us suppose that the motorist starts from point P and then he takes the third turn at S....
A cyclist starts from the centre O of a circular park of radius 1 km, reaches the edge P of the park, then cycles along the circumference, and returns to the centre along QO as shown in Fig. 4.21. If the round trip takes 10 min, what is the (i) Net displacement (ii) Average velocity and (iii) The average speed of the cyclist.
Answer - (i) Displacement refers to the distance between the body's original and ultimate positions. In 20 minutes, the cyclist returns to the point where he began. As a result, there is no...
Three girls skating on a circular ice ground of radius 200 m start from a point P on the edge of the ground and reach a point Q diametrically opposite to P following different paths as shown in Fig. 4.20. What is the magnitude of the displacement vector for each? For which girl is this equal to the actual length of path skate?
Answer - The smallest distance between a particle's initial and final coordinates determines displacement. In the example, all of the girls begin at point P and work their way to point Q. Their...
Given that l + m + n + o = 0, which of the given statements are true: (c) The magnitude of l can never be greater than the sum of the magnitudes of m, n and o. (d) m + n must lie in the plane of l and o if l and o are not collinear, and in the line of l and o, if they are collinear?
Answer - (c) True We can write the given equation as => l = (m + n + o) Taking mode on both the sides, we get - | l | = | m + n + o | or | l | <= | m + n + o | The magnitude of l is equal to...
Given that l + m + n + o = 0, which of the given statements are true: (a) l, m, n and o each must be a null vector. (b) The magnitude of (l + n) equals the magnitude of (m+ o).
Answer - (a) False It is not necessary for all four supplied vectors to be null vectors in order for l + m + n + o = 0. There are more combinations that can result in a zero sum. (b) True l + m + n...
Establish the following vector inequalities geometrically or otherwise:
\[\left| \vec{a}-\vec{b} \right|\ge \left| \left| {\vec{a}} \right|-\left| {\vec{b}} \right| \right|\] Answer - Let two vectors $\vec{a}$and $\vec{b}$represent two adjacent sides of a parallelogram...
Establish the following vector inequalities geometrically or otherwise:
\[\left| \vec{a}-\vec{b} \right|\le \left| {\vec{a}} \right|+\left| {\vec{b}} \right|\] Answer - Let two vectors $\vec{a}$and $\vec{b}$represent two adjacent sides of a parallelogram PQRS, as show...
Establish the following vector inequalities geometrically or otherwise:
\[\left| \vec{a}+\vec{b} \right|\ge \left| \left| {\vec{a}} \right|-\left| {\vec{b}} \right| \right|\] Answer : Let two vectors $\vec{a}$and $\vec{b}$represent two adjacent sides of a parallelogram...
Establish the following vector inequalities geometrically or otherwise:
\[\left| \overrightarrow{a}+\overrightarrow{b} \right|\le \left| \overrightarrow{a} \right|+\left| {\vec{b}} \right|\] Answer - Let two vectors $\vec{a}$and $\vec{b}$represent two adjacent sides of...
A metre stick is balanced on a knife-edge at its centre. When two coins, each of mass are put one on top of the other at the mark, the stick is found to be balanced at . What is the mass of the metre stick?
When two coins are inserted at the 12 cm point, the metre rule's centre of mass shifts to 45 cm from 50 cm. Mass of two coins is given as $m=10 \mathrm{~g}$ The distance at which the coins are...
From a uniform disc of radius , a circular hole of radius is cut out. The centre of the hole is at from the centre of the original disc. Locate the centre of gravity of the resulting flat body
Let the unit area of the original disc be $\sigma$ The radius of the original disc is given as $2r$ Mass of the original disc can be calculated as $m=\pi\left(2 r^{2}\right) \sigma=4 \pi r^{2}...
To maintain a rotor at a uniform angular speed of , an engine needs to transmit a torque of What is the power required by the engine? (Note: uniform angular velocity in the absence of friction implies zero torque. In practice, applied torque is needed to counter frictional torque). Assume that the engine is efficient.
The angular speed of the rotor is given as $\omega=200 \mathrm{rad} / \mathrm{s}$ Torque is given as $T=180 \mathrm{Nm}$ So, power of the rotor (P) can be calculated as, $P=T \omega$ $=200 \times...
A rope of negligible mass is wound around a hollow cylinder of mass and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N? What is the linear acceleration of the rope? Assume that there is no slipping.
Mass of the hollow cylinder is given as $m=3 \mathrm{~kg}$ Radius of the hollow cylinder is given as $r=40 \mathrm{~cm}=0.4 \mathrm{~m}$ So, force applied will be $F=30 \mathrm{~N}$ Calculating the...
(a) A child stands at the centre of a turntable with his two arms outstretched. The turntable is set rotating with an angular speed of . How much is the angular speed of the child if he folds his hands back and thereby reduces his moment of inertia to times the initial value? Assume that the turntable rotates without friction
(b) Show that the child’s new kinetic energy of rotation is more than the initial kinetic energy of rotation. How do you account for this increase in kinetic energy?
(a) Initial angular velocity, is given as $\omega_{1}=40 \mathrm{rev} / \mathrm{min}$ Suppose the final angular velocity be $\omega_{2}$ Let the moment of inertia of the boy with stretched hands be...
A solid cylinder of mass rotates about its axis with angular speed . The radius of the cylinder is . What is the kinetic energy associated with the rotation of the cylinder? What is the magnitude of angular momentum of the cylinder about its axis?
Mass of the cylinder is given as $m=20 \mathrm{~kg}$ Angular speed is given as $\omega=100 \mathrm{rad} \mathrm{s}^{-1}$ Radius of the cylinder is given as $r=0.25 \mathrm{~m}$ So, the moment of...
Torques of equal magnitude are applied to a hollow cylinder and a solid sphere, both having the same mass and radius. The cylinder is free to rotate about its standard axis of symmetry, and the sphere is free to rotate about an axis passing through its centre. Which of the two will acquire a greater angular speed after a given time?
Let the mass radius of the solid sphere and also the hollow cylinder be m and r. The moment of inertia of the hollow cylinder about its standard axis is given as ${{I}_{1}}=M{{R}^{2}}$ Moment of...
(a) Find the moment of inertia of a sphere about a tangent to the sphere, given the moment of inertia of the sphere about any of its diameters to be , where is the mass of the sphere and is the radius of the sphere.
(b) Given the moment of inertia of a disc of mass M and radius about any of its diameters to be , find its moment of inertia about an axis normal to the disc and passing through a point on its edge.
The moment of inertia of a sphere about its diameter is $=2 \mathrm{MR}^{2} / 5$ and is also shown in the figure, As the the theorem of parallel axes says, M.I of a sphere about a tangent to the...
A car weighs . The distance between its front and back axles is . Its centre of gravity is behind the front axle. Determine the force exerted by the level ground on each front wheel and each back wheel.
Mass of the car is given as $m=1800 \mathrm{~kg}$ Distance between the two axles is given as $d=1.8 \mathrm{~m}$ Distance of the centre of gravity from the front axle is given as $=1.05 \mathrm{~m}$...
A irregular plank weighing is suspended in the manner shown below, by strings of negligible weight. If the strings make an angle of and respectively with the vertical, find the location of center of gravity of the plank from the left end.
Following is the FBD(Free Body Diagram) for the above figure: Length of the plank is given as $\mid=2 \mathrm{~m}$ $\theta_{1}=35^{\circ}$ and $\theta_{2}=55^{\circ}$ Let the tensions produced in...
Two particles, each of mass and speed v, travel in opposite directions along parallel lines separated by a distance . Show that the angular momentum vector of the two-particle system is the same whatever be the point about which the angular momentum is taken
Considering three points $Z, C$ and $X$ : Angular momentum at Z will be given as, $\mathrm{Lz}=\mathrm{mv} \times 0+\mathrm{mv} \times \mathrm{d}$ $=\mathrm{mvd}-(1)$ Angular momentum about $x$ will...
Find the components along the axes of the angular momentum I of a particle, whose position vector is with components and momentum is with components and . Show that if the particle moves only in the plane the angular momentum has only a zcomponent.
Linear momentum is given by $\vec{p}=p_{x} \hat{i}+p_{y} \hat{j}+p_{z} \hat{k}$ Positional vector of the body is given by $\vec{r}=x \hat{i}+y \hat{j}+z \hat{k}$ Angular momentum is given by...
Show that is equal in magnitude to the volume of the parallelepiped formed on the three vectors, and .
Let the parallelepiped formed be: where, $\overrightarrow{O J}=\vec{a}, \overrightarrow{O L}=\vec{b}$ and $\overrightarrow{O K}=\vec{c}$ $\hat{n}$ is a unit vector along $\mathrm{OJ}$ and is...
Show that the area of the triangle contained between the vectors a and is one half of the magnitude of
The side $A D$ is equal to $\vec{a}$ and $A B$ is equal to $\vec{b}$ For $\triangle \mathrm{ADN}$ : $\sin \theta=\mathrm{DN} / \mathrm{AD}=\mathrm{DN} / \vec{a}$ $\mathrm{DN}=\vec{a} \sin \theta$...
A child sits stationary at one end of a long trolley moving uniformly with a speed on a smooth horizontal floor. If the child gets up and runs about on the trolley in any manner, what is the speed of the CM of the (trolley + child) system?
The child and the trolley are one system, and the youngster's movement within the cart is entirely internal. The velocity of the system's centre of mass will not change because there is no external...
In the HCI molecule, the separation between the nuclei of the two atoms is about ). Find the approximate location of the CM of the molecule, given that a chlorine atom is about times as massive as a hydrogen atom and nearly all the mass of an atom is concentrated in its nucleus.
Mass of hydrogen atom is known as $1$ unit Mass of chlorine atom is known as $35.5$ unit Let the center of mass to be $x$ metre from the chlorine atom So, the distance of center of mass from the...
Give the location of the centre of mass of a (i) sphere, (ii) cylinder, (iii) ring, and (iv) cube, each of uniform mass density. Does the centre of mass of a body necessarily lie inside the body?
All of the structures are symmetrical bodies with a fairly consistent mass density. As a result, the centre of mass for all of the above bodies will be in their geometric centres. The centre of mass...
A rocket is fired ‘vertically’ from the surface of mars with a speed of . If of its initial energy is lost due to martian atmospheric resistance, how far will the rocket go from the surface of mars before returning to it? Mass of mars radius of mars ; G
Velocity of the rocket fired from the surface of $\operatorname{mars}(v)=2 \mathrm{~km} / \mathrm{s}$ Let $m$ be the mass of the rocket Mass of the Mars is given as $(M)=6.4 \times 10^{23}...
A spaceship is stationed on Mars. How much energy must be expended on the spaceship to launch it out of the solar system? Mass of the space ship kg; mass of the sun = kg; mass of mars kg; radius of mars ; radius of the orbit of mars
Mass of the spaceship is given as $m_{s}=1000 \mathrm{~kg}$ Mass of the Sun is given as $M=2 \times 10^{30} \mathrm{~kg}$ Mass of Mars is given as $m_{m}=6.4 \times 10^{23} \mathrm{~kg}$ Radius of...
A star times the mass of the sun and collapsed to a size of 12 km rotates with a speed of rev. per second. (Extremely compact stars of this kind are known as neutron stars. Certain stellar objects called pulsars belong to this category). Will an object placed on its equator remain stuck to its surface due to gravity? (mass of the sun ).
If the outward centrifugal force is lesser than the inward gravitational pull, any matter will remain stuck to the surface. Gravitational force is given by the relation: $f_{G}=\frac{G M m}{R^{2}}$...
As you have learnt in the text, a geostationary satellite orbits the earth at a height of nearly from the surface of the earth. What is the potential due to earth’s gravity at the site of this satellite? (Take the potential energy at infinity to be zero). Mass of the earth = , radius .
Radius of the Earth is given as $R=6400 \mathrm{~km}=0.64 \times 10^{7} \mathrm{~m}$ Mass of Earth is known as $M=6 \times 10^{24} \mathrm{~kg}$ Height of the geostationary satellite from earth's...
Two heavy spheres each of mass and radius are placed apart on a horizontal table. What is the gravitational force and potential at the midpoint of the line joining the centres of the spheres? Is an object placed at that point in equilibrium? If so, is the equilibrium stable or unstable?
Radius of spheres is given as $R=0.10 \mathrm{~m}$ Distance between two spheres is given as $r=1.0 \mathrm{~m}$ Mass of each sphere is given as $M=100 \mathrm{~kg}$ We can infer from the figure that...
Two stars each of one solar mass are approaching each other for a headon collision. When they are a distance , their speeds are negligible. What is the speed with which they collide? The radius of each star is Assume the stars to remain undistorted until they collide. (Use the known value of G).
Mass of each star is given as $M=2 \times 10^{30} \mathrm{~kg}$ Radius of each star is given as $R=10^{4} \mathrm{~km}=10^{7} \mathrm{~m}$ Distance between the stars is given as $r=10^{9}...
A satellite orbits the earth at a height of above the surface. How much energy must be expended to rocket the satellite out of the earth’s gravitational influence? Mass of the satellite kg; mass of the earth kg; radius of the earth
Height of the satellite is given as $h=400 \mathrm{~km}=4 \times 10^{5} \mathrm{~m}$ Mass of the Earth is known as $M=6.0 \times 10^{24} \mathrm{~kg}$ Mass of the satellite is given as $m=200...
The escape speed of a projectile on the earth’s surface is . A body is projected out with thrice this speed. What is the speed of the body far away from the earth? Ignore the presence of the sun and other planets.
Escape velocity of the projectile on the Earth's surface is given as $\mathrm{V}_{\mathrm{e}}=11.2 \mathrm{~km} / \mathrm{s}$ Velocity of projection of the body will be, $v=3 \mathrm{Ve}=3 \times...
A rocket is fired vertically with a speed of from the earth’s surface. How far from the earth does the rocket go before returning to the earth? Mass of the earth ; mean radius of the earth
Velocity of the missile is given as $v=5 \times 10^{3} \mathrm{~m} / \mathrm{s}$ Mass of the Earth is known as $M_{E}=6 \times 10^{24} \mathrm{~kg}$ Radius of the Earth is given as $R_{E}=6.4 \times...
Thermodynamics isn’t worried about______. (I) energy changes associated with a substance response. (ii) the degree to which a substance response continues. (iii) the rate at which a response continues. (iv) the practicality of a synthetic response.
solution: Choice (iii) is the appropriate response. This is because Thermodynamics informs us concerning the practicality, energy changes and degree of compound response. It doesn't informs us...
Assuming the earth to be a sphere of uniform mass density, how much would a body weigh halfway down to the centre of the earth if it weighed on the surface?
Weight of a body on the Earth's surface is given as $W=m g=250 \mathrm{~N}$ Let $R_{e}$ be the radius of the earth Let $d$ be at a distance halfway to the centre of the earth, then, $d=R_{e} / 2$...
A body weighs on the surface of the earth. What is the gravitational force on it due to the earth at a height equal to half the radius of the earth?
Weight of the man is given as $W=63 \mathrm{~N}$ Acceleration due to gravity at height 'h' from the Earth's surface is: g'=g1+hRe2...
A Saturn year is times the Earth year. How far is the Saturn from the Sun if the Earth is away from the Sun?
According to Kepler's third law of planetary motion, the following relation can be written, $T=\sqrt{\frac{4 \pi^{2} r^{3}}{G M}}$ We get $\mathrm{T}^{2} \propto \mathrm{r}^{3}$ from the above...
How will you ‘weigh the sun’, that is estimate its mass? The mean orbital radius of the earth around the sun is .
Earth's orbit has a radius of $r=1.5 \times 10^{11} \mathrm{~m}$ Time taken by the Earth for one complete revolution can be $\mathrm{T}=1$ year $=365.25$ days i.e. $T=(365.25 \times 24 \times 60...
A rocket is fired from the earth towards the sun. At what distance from the earth’s centre is the gravitational force on the rocket zero? Mass of the sun , mass of the earth x . Neglect the effect of other planets etc. (orbital radius ).
Mass of Sun is given as $M_{\text {sun }}=2 \times 10^{30} \mathrm{~kg}$ Mass of Earth is given as $M_{\text {earth }}=6 \times 10^{24} \mathrm{~kg}$ Orbital radius is given as $r=1.5 \times 10^{11}...
Choose the correct answer from among the given ones: the direction of the gravitational intensity at an arbitrary point is indicated by the arrow (i) , (ii) e, (iii) f, (iv) .
(ii) e Reason: From the previous response, we can deduce that, The gravitational intensity at P is directed downwards along 'e' using the logic/explanation
Choose the correct answer from among the given ones: The gravitational intensity at the centre of a hemispherical shell of uniform mass density has the direction indicated by the arrow (see Fig) (i) a, (ii) , (iii) c, (iv) 0
(iii) $\mathrm{C}$ Reason: Gravitational forces on any particle at any position are symmetrically distributed inside a hollow sphere. The upper half of the sphere is, however, deleted in this...
Which of the following symptoms is likely to afflict an astronaut in space
(a) headache,
(b) orientational problem.
(a). Astronauts may get headaches as a result of the increased blood supply to their faces. (b). Because space has multiple orientations, an astronaut may experience orientational issues.
Which of the following symptoms is likely to afflict an astronaut in space
(a) swollen feet,
(b) swollen face
(a) Because blood flow to the feet is not increased in zero gravity, the astronaut's feet do not swell. (b) There is more blood supply to the astronaut's face. As a result, the astronaut's face will...
A comet orbits the Sun in a highly elliptical orbit.
(a) potential energy
(b) total energy throughout its orbit? Neglect any mass loss of the comet when it comes very close to the Sun.
(a) Potential energy changes along the path. (b) Total energy will remain constant throughout the orbit.
A comet orbits a sun in a highly elliptical orbit. Does the comet have a constant
(a) linear speed,
(b) angular speed,
(c) angular momentum,
(d) kinetic energy,
(e) potential energy,
(f) total energy throughout its orbit? Neglect any mass loss of the comet when it comes very close to the sun.
A comet in an elliptical orbit around the Sun has constant angular momentum and total energy owing to the Law of Conservation of Energy at all locations, but other variables change. The torque...
A comet orbits the Sun in a highly elliptical orbit. Does the comet have a constant
(a) linear speed
(b) angular speed
(a) The linear speed of the comet changes according to Kepler's second law. The comet's speed will be the quickest when it is closest to the sun, and the slowest when it is farthest away. (b)...
Does the escape speed of a body from the earth depend on
(a) the direction of projection,
(b) the height of the location from where the body is launched?
The escape speed can be given by the relation, $v=\sqrt{\frac{2 G M}{R}}=\sqrt{2 g R}$ (a) The escape speed does not depend on the direction of projection of a body. (b) Because the escape velocity...
Q. 7. Does the escape speed of a body from the earth depend on
(a) the mass of the body,
(b) the location from where it is projected
The escape speed can be given by the relation, $v=\sqrt{\frac{2 G M}{R}}=\sqrt{2 g R}$ (a) The mass of a body has no bearing on its speed of departure from the Earth. (b) The escape speed of a body...
Choose the correct alternative:
(a) If the zero of potential energy is at infinity, the total energy of an orbiting satellite is negative of its kinetic/potential energy.
(b) The energy required to launch an orbiting satellite out of earth’s gravitational influence is more/less than the energy required to project a stationary object at the same height (as the satellite) out of earth’s influence.
(a) The total energy of an orbiting satellite is negative of its kinetic energy if the zero potential energy is at infinity. (b) The energy required to launch an orbiting satellite out of Earth's...
Explain why (c) Hydrostatic pressure is a scalar quantity even though the pressure is force divided by area
Answer : Answer : (c). In hydrostatic pressure, the force is transmitted in all directions of the fluid equally so there is no fixed pressure direction, making it a scalar quantity.
Let us assume that our galaxy consists of stars each of one solar mass. How long will a star at a distance of ly from the galactic centre take to complete one revolution? Take the diameter of the Milky Way to be .
Mass of our galaxy is given as $M=2.5 \times 10^{11}$ solar mass 1 Solar mass as we know is, Mass of Sun $=2 \times 10^{30} \mathrm{~kg}$ Mass of our galaxy as we know is $M=2.5 \times 10^{11}...
lo, one of the satellites of Jupiter, has an orbital period of days and the radius of the orbit is Show that the mass of J upiter is about one-thousandth that of the sun.
Orbital period of $I0$, is given as $T_{10}=1.769$ days $=1.769 \times 24 \times 60 \times 60 \mathrm{~s}$ Orbital radius of $I0$, is given as $R_{10}=4.22 \times 10^{8} \mathrm{~m}$ Mass of jupiter...
Explain why (a) The blood pressure in humans is greater at the feet than at the brain (b) Atmospheric pressure at a height of about 6 km decreases to nearly half of its value at the sea level, though the height of the atmosphere is more than 100 km
Answer : (a). The blood column in the legs is higher than the head, so the blood pressure in the legs is higher than the brain. (b). The density of the atmosphere does not decrease linearly with...
Suppose there existed a planet that went around the Sun twice as fast as the earth. What would be its orbital size as compared to that of the earth?
Time taken by the earth for one complete revolution is represented by $\mathrm{T}_{\mathrm{E}}$ having value $1$ Year Radius of Earth's orbit is represented by $\mathrm{R}_{\mathrm{E}}$ having value...
Choose the correct alternative:
(a) Acceleration due to gravity is independent of the mass of the earth/mass of the body.
(b) The formula is more/less accurate than the formula for the difference of potential energy between two points and distance away from the centre of the earth.
(a) Acceleration due to gravity is given by the formula: $g=G{{M}_{e}} /{{ {R}_{e}}^{2}}$ is Hence, it is independent of mass of body, but is dependent on mass of earth. (b) Gravitational...
Read each statement below carefully and state with reasons, if it is true or false: (e) Three vectors not lying in a plane can never add up to give a null vector.
Answer : (e) True : The three vectors are not in a plane, it is not possible to represent the sides of a triangle in the same order.
Choose the correct alternative:
(a) Acceleration due to gravity increases/decreases with increasing altitude.
(b) Acceleration due to gravity increases/decreases with increasing depth (assume the earth to be a sphere of uniform density).
(a) According to the formula g′=g(1-R2h), acceleration decreases. where h is the height and R is the earth's radius (b) According to the formula g′=g(1−Rd),, acceleration decreases. where d is the...
Read each statement below carefully and state with reasons, if it is true or false: (c) The total path length is always equal to the magnitude of the displacement vector of a particle (d) The average speed of a particle (defined as total path length divided by the time taken to cover the path) is either greater or equal to the magnitude of the average velocity of the particle over the same interval of time
Answer : (c) False: The total length of the path is a scalar quantity, and the displacement is a vector quantity. Therefore, the total length of the path is always greater than the amplitude of the...
Isostructural species are those which have the same shape and hybridisation. Among the given species identify the isostructural pairs. (i) [NF3 and BF3] (ii) [BF4- and NH4+] (iii) [BCl3 and BrCl3] (iv) [NH3 and NO3-]
From a structural standpoint, we can see that, NF3 is pyramidal whereas BF3 is planar triangular. BF4- and NH4+ ions are tetrahedral in structure. BCl3 is triangular planar and BrCl3 is...
Read each statement below carefully and state with reasons, if it is true or false: (a) The magnitude of a vector is always a scalar (b) Each component of a vector is always a scalar
Answer : a) True: The magnitude of the vector is a number. Hence it is a scalar quantity. (b) False: Every component of a vector is also a vector.
Answer the following: If you compare the gravitational force on the earth due to the sun to that due to the moon, you would find that the Sun’s pull is greater than the moon’s pull. (you can check this yourself using the data available in the succeeding exercises). However, the tidal effect of the moon’s pull is greater than the tidal effect of the sun. Why?
Tidal effects are inversely proportional to the cube of distance, whereas gravitational force is inversely proportional to the square of distance. The moon will have a stronger influence on the...
Answer the following: (a) You can shield a charge from electrical forces by putting it inside a hollow conductor. Can you shield a body from the gravitational influence of nearby matter by putting it inside a hollow sphere or by some other means? (b) An astronaut inside a small space ship orbiting around the earth cannot detect gravity. If the space station orbiting around the earth has a large size, can he hope to detect gravity?
(a). No, no technology has yet been devised to shield a body from gravity because gravity is a property of all matter and is independent of medium. As a result, the gravitational forces would be...
State with reasons, whether the following algebraic operations with scalar and vector physical quantities are meaningful : (a) Addition of any two scalars (b) Adding a scalar to a vector which has the same dimensions (c) Multiplying a vector by any scalar (d) Multiplying any two scalars (e) Adding any two vectors (f) Addition of a vector component to the same vector.
Answer : (a) Meaningful: Adding two scalar quantities makes sense only if they both represent the same physical quantity. (b) Not Meaningful: The addition of a vector quantity to a scalar quantity...
From the following identify the vector quantities : Pressure, temperature, energy, time, gravitational potential, power, total path length, charge, coefficient of friction, impulse.
Answer : Impulse is the product of force and time. Since force is a vector, its time product is a scalar, giving a vector.
From the following pick any two scalar quantities: Force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, relative velocity.
Answer : The scalar product of force and path is the work done. Work is a scalar because the scalar product of two quantities is always a scalar. The current is a scalar, because it is only...
Among halogens, the correct order of the amount of energy released in electron gain (electron gain enthalpy) is:
(i) F > Cl > Br > I
(ii) F < Cl < Br < I
(iii) F < Cl > Br > I
(iv) F < Cl < Br < I
Option (iii) is the answer. The amount of energy released when an electron is added to an isolated gaseous atom is known as electron gain enthalpy. The electron gain enthalpy of F is less...
State whether the following physical quantities are scalar or vector. (i) Mass (ii) Volume (iii) Speed (iv) Acceleration (v) Density (vi) Number of moles (vii) Velocity (viii) Angular frequency (ix) Displacement (x) Angular velocity
Answer : Scalar: Density, mass, speed, volume, angular frequency, number of moles. Vector: Velocity, acceleration, angular velocity, displacement. A scalar quantity is determined solely by its...
The electronic configuration of gadolinium (Atomic number 64) is
Option (iii) is the answer. The electronic configuration of gandolium is [Xe] 4f7 5d1 6s2
The correct formulae describing the motion of the particle are (c), (d) and, (f) The given graph has a non-uniform slope. Hence, the formulae given in (a), (b), and (e) cannot describe the motion of the particle. Only relations given in (c), (d), and (f) are correct equations of motion.
Answer : (c), (d), and (e) are the correct formulae for characterizing the particle's motion (f) The given graph has a non-uniform slope. As a result, the formulas in (a), (b), and (e) are unable to...