NCERT

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,...

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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...

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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...

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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.

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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...

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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...

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Separation of Motion of a system of particles into motion of the centre of mass and motion about the centre of mass:
(i) Show L=L^{\prime}+R \times M V where L^{\prime}=\Sigma r^{\prime}{ }_{i} \times p_{i}^{\prime} is the angular momentum of the system about the centre of mass with velocities considered with respect to the centre of mass. Note r_{i}=r_{i}-R, rest of the notation is the standard notation used in the lesson. Note L’ and MR \times V can be said to be angular momenta, respectively, about and of the centre of mass of the system of particles.
(ii) Prove that : \mathrm{dL}^{\prime} / \mathrm{dt}=\sum \mathrm{r}_{\mathrm{i}}^{\prime} \mathrm{x} \mathrm{dp}^{\prime} / \mathrm{dt} Further prove that: \mathrm{dL}^{\prime} / \mathrm{dt}=\mathrm{T}^{\prime} \mathrm{ext} 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...

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Separation of Motion of a system of particles into motion of the centre of mass and motion about the centre of mass:
(i) Show p=p_{i}^{\prime}+m_{i} V Where p_{i} is the momentum of the i^{\text {th }} particle (of mass \left.m_{i}\right) and p_{i}=m_{i} v_{i}^{t} . Note v_{i}^{\prime} is the velocity of the \mathrm{i}^{\mathrm{ith}} particle with respect to the centre of mass.Also, verify using the definition of the centre of mass that \Sigma p_{i}=0
(ii) Prove that \mathrm{K}=\mathrm{K}^{\prime}+1 / 2 \mathrm{MV}^{2} Where K is the total kinetic energy of the system of particles, K^{\prime} is the total kinetic energy of the system when the particle velocities are taken relative to the center of mass and \mathrm{MV}^{2} / 2 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...

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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.

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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...

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A cylinder of mass 10 \mathrm{~kg} and radius 15 \mathrm{~cm} is rolling perfectly on a plane of inclination 30^{\circ} . The coefficient of static friction \mu_{\mathrm{s}}=0.25. If the inclination \theta of the plane is increased, at what value of \theta 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...

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A cylinder of mass 10 \mathrm{~kg} and radius 15 \mathrm{~cm} is rolling perfectly on a plane of inclination 30^{\circ} . The coefficient of static friction \mu_{\mathrm{s}}=0.25
(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...

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A solid disc and a ring, both of radius 10 \mathrm{~cm} are placed on a horizontal table simultaneously, with an initial angular speed equal to 10 \mathrm{~m} \mathrm{rad} \mathrm{s}^{-1}. Which of the two will start to roll earlier? The coefficient of kinetic friction is \mu_{k}=0.2 .

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...

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A disc rotating about its axis with angular speed \omega_{0} 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 A, B and C 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...

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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 h is given by \mathrm{v}^{2}=2 \mathrm{gh} /\left(1+\mathrm{k}^{2} / \mathrm{R}^{2}\right) using dynamical consideration (i.e. by consideration of forces and torques). Note \mathrm{k} is the radius of gyration of the body about its symmetry axis, and \mathbf{R} 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...

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(a) Prove the theorem of perpendicular axes. (Hint: Square of the distance of a point (x, y) in the x-y plane from an axis through the origin and perpendicular to the plane is \left.x^{2}+y^{2}\right).
(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 \left.\sum m_{i} r_{i}=0\right).

(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...

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Two discs of moments of inertia I_{1} and I_{2} about their respective axes (normal to the disc and passing through the centre), and rotating with angular speeds \omega_{1} and \omega_{2} 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 \omega_{1} \neq \omega_{2}

(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...

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A bullet of mass 10 \mathrm{~g} and speed \mathbf{5 0 0} \mathrm{m} / \mathrm{s} is fired into a door and gets embedded exactly at the centre of the door. The door is 1.0 \mathrm{~m} wide and weighs 12 \mathrm{~kg}. 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...

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A man stands on a rotating platform, with his arms stretched horizontally holding a 5 \mathrm{~kg} 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 90 \mathrm{~cm} to 20 \mathrm{~cm}. The moment of inertia of the man together with the platform may be taken to be constant and equal to 7.6 \mathrm{~kg} \mathbf{m}^{2}.
(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,...

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As shown in Figure the two sides of a step ladder BA and CA are 1.6 \mathbf{m} long and hinged at A. A rope DE, 0.5 m is tied halfway up. A weight 40 \mathrm{~kg} is suspended from a point F, 1.2 \mathrm{~m} 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 g=9.8 \mathrm{m} / \mathbf{s}^{2} ) (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...

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A solid cylinder rolls up an inclined plane of the angle of inclination 30^{\circ} . At the bottom of the inclined plane, the centre of mass of the cylinder has a speed of 5 \mathrm{~m} / \mathrm{s}.
(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:...

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The oxygen molecule has a mass of 5.30 \times 10^{-26} \mathrm{~kg} and a moment of inertia of 1.94 \times 10^{-46} \mathrm{~kg} m^{2} 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 \mathbf{5 0 0} \mathbf{m} / \mathbf{s} 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...

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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...

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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.

    \[\begin{array}{*{35}{l}}    \left( I \right)\text{ }w\text{ }\left( reversible \right)\text{ }=\text{ }w\text{ }\left( irreversible \right)  \\    ~  \\    \left( ii \right)\text{ }w\text{ }\left( reversible \right)\text{ }<\text{ }w\text{ }\left( irreversible \right)  \\    ~  \\    \left( iii \right)\text{ }w\text{ }\left( reversible \right)\text{ }>\text{ }w\text{ }\left( irreversible \right)  \\    ~  \\    \left( iv \right)\text{ }w\text{ }\left( reversible \right)\text{ }=\text{ }w\text{ }\left( irreversible \right)\text{ }+\text{ }pex.V  \\ \end{array}\]

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...

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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?

    \[\left( Considering\text{ }that\text{ }1\text{ }L\text{ }bar\text{ }=\text{ }100J \right)\]

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(...

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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?

    \[H2\left( g \right)\text{ }+\text{ }Br2\left( g \right)\text{ }\to \text{ }2HBr\left( g \right)\]

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{...

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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...

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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...

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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...

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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,...

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. 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...

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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{...

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. Think about the accompanying response among zinc and oxygen and pick the right alternatives out of the choices given underneath :

    \[2\text{ }Zn\text{ }\left( s \right)\text{ }+\text{ }O2\text{ }\left( g \right)\text{ }\to \text{ }2\text{ }ZnO\text{ }\left( s \right)\text{ };\text{ }H\text{ }=\text{ }\text{ }693.8\text{ }kJ\text{ }mol1\]

(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

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. For an optimal gas, crafted by reversible extension under isothermal condition can be determined by utilizing the articulation

    \[w\text{ }=\text{ }\text{ }nRT\text{ }ln\text{ }Vf/Vi\]

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...

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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...

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. 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...

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. 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...

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The entropy change can be determined by utilizing the articulation

    \[S\text{ }=\text{ }qrev/T\]

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...

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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.

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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.

    \[\begin{array}{*{35}{l}}    \left( I \right)\text{ }q\text{ }=\text{ }0,\text{ }T\text{ }\ne \text{ }0,\text{ }w\text{ }=\text{ }0  \\    ~  \\    \left( ii \right)\text{ }q\text{ }\ne \text{ }0,\text{ }T\text{ }=\text{ }0,\text{ }w\text{ }=\text{ }0  \\    ~  \\    \left( iii \right)\text{ }q\text{ }=\text{ }0,\text{ }T\text{ }=\text{ }0,\text{ }w\text{ }=\text{ }0  \\    ~  \\    \left( iv \right)\text{ }q\text{ }=\text{ }0,\text{ }T\text{ }<\text{ }0,\text{ }w\text{ }\ne \text{ }0  \\ \end{array}\]

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,  ...

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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...

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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...

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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...

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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...

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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...

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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 :...

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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...

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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....

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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...

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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...

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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...

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To maintain a rotor at a uniform angular speed of 200 \mathrm{rad} \mathrm{s}^{-1}, an engine needs to transmit a torque of 180 \mathrm{~N} \mathrm{~m} . 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 100 \% 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...

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A rope of negligible mass is wound around a hollow cylinder of mass 3 \mathbf{k g} 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...

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(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 40 \mathrm{rev} / \mathrm{min}. How much is the angular speed of the child if he folds his hands back and thereby reduces his moment of inertia to 2 / 5 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...

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A solid cylinder of mass 20 \mathrm{~kg} rotates about its axis with angular speed 100 \mathrm{rad} \mathrm{s}^{-1}. The radius of the cylinder is 0.25 \mathrm{~m}. 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...

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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...

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(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 2 \mathrm{MR}^{2} / 5, where M is the mass of the sphere and \mathbf{R} is the radius of the sphere.
(b) Given the moment of inertia of a disc of mass M and radius \mathbf{R} about any of its diameters to be \mathrm{MR}^{2} / 4, 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...

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A 2 \mathrm{~m} irregular plank weighing \mathrm{W} \mathrm{kg} is suspended in the manner shown below, by strings of negligible weight. If the strings make an angle of 35^{0} and 55^{\circ} 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...

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Two particles, each of mass m and speed v, travel in opposite directions along parallel lines separated by a distance d. 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...

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Find the components along the x, y, z axes of the angular momentum I of a particle, whose position vector is r with components x, y, z and momentum is p with components p_{x}, p_{y} and p_{z}. Show that if the particle moves only in the x-y 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...

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A child sits stationary at one end of a long trolley moving uniformly with a speed \mathbf{V} 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...

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In the HCI molecule, the separation between the nuclei of the two atoms is about 1.27 \AA(1 \AA =10^{-10} \mathrm{~m} ). Find the approximate location of the CM of the molecule, given that a chlorine atom is about 35.5 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...

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A rocket is fired ‘vertically’ from the surface of mars with a speed of 2 \mathrm{~km} \mathrm{~s}^{-1}. If 20 \% 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 =6.4 \times 10^{23} \mathrm{~kg} ; radius of mars =3395 \mathrm{~km}; G =6.67 \times 10^{-11} \mathrm{~N} \mathrm{~m}^{2} \mathrm{~kg}^{-2} .

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}...

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A star 2.5 times the mass of the sun and collapsed to a size of 12 km rotates with a speed of 1.2 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 =2 \times 10^{30} \mathrm{~kg} ).

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: $f_{G}=\frac{G M m}{R^{2}}$...

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As you have learnt in the text, a geostationary satellite orbits the earth at a height of nearly 36,000 \mathrm{~km} 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 = 6.0 \times 10^{24} \mathrm{~kg}, radius =\mathbf{6 4 0 0} \mathrm{km}.

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...

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Two heavy spheres each of mass 100 \mathrm{~kg} and radius 0.10 \mathrm{~m} are placed 1.0 \mathrm{~m} 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...

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Two stars each of one solar mass \left(=2 \times 10^{30} \mathrm{~kg}\right) are approaching each other for a headon collision. When they are a distance 10^{9} \mathrm{~km}, their speeds are negligible. What is the speed with which they collide? The radius of each star is 10^{4} \mathrm{~km} . 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}...

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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...

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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...

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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...

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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...

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Choose the correct alternative:
(a) Acceleration due to gravity is independent of the mass of the earth/mass of the body.
(b) The formula -G\mathrm{M} \mathbf{m}\left(1 / \mathbf{r}_{2}-1 / \mathbf{r}_{1}\right) is more/less accurate than the formula \mathrm{mg}\left(\mathrm{r}_{2}-\mathrm{r}_{1}\right) for the difference of potential energy between two points r_{2} and r_{1} 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...

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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...

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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...

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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...

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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...

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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...

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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...

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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...

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