Lakhmir Singh

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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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 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) What is meant by “electric power”? Write the formula for electric power in terms of potential difference and current. b) The diagram below shows a circuit containing a lamp L, a voltmeter, and an ammeter. The voltmeter reading is 3V and the ammeter reading is 0.5A. What is the resistance and power of the lamp?

Answer: a) The rate at which electrical energy is consumed is referred to as electric power. It is given as: P = VI = watt b) Given in the question, V =...

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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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(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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The diagram below depicts an electric circuit in which current passes via two resistors from a 6V battery. a)The two resistors share the current that flows from the battery. Which resistor will receive the majority of the current? b) Determine the two resistors’ effective resistance.

answer: Given, V = 6V R1 = 2Ω R2 = 3 Ω a)Because of its lower resistance, 2 ohm resistance has a larger share of current. b) Effective resistance = R 1/R = ½ + 1/3 1/R = 5/6 R = 1.2...

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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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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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Two resistance coils A and B of 24 ohm resistance each are linked to a 220V supply line on an electric heater. These coils can be utilised in a series or parallel configuration. Calculate the current drawn in the following situation: coils A and B are used in parallel

When coils A and B are utilised in parallel, the current drawn is: Total resistance is 1/R = 1/Ra + 1/Rb = 1/24 + 1/24 = 2/24 = 1/12 R = 12 ohms I = V/R = 220/12 = 18.33 amps

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Two resistance coils A and B of 24 ohm resistance each are linked to a 220V supply line on an electric heater. These coils can be utilised in a series or parallel configuration. Calculate the current drawn in the following situations: a) Only one coil A is utilized; b) coils A and B are connected in series

answer: given Ra = Rb = 24 ohm a) Current drawn when coil A is the only one used: I = V/Ra = 220/24 = 9.16 amps b) Current drawn in series when coils A and B are used: Total resistance, R = Ra + Rb...

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Two resistors with resistances of 5 and 10 should be connected to a 6V emf battery to get the minimum and maximum current flowing. a) In each situation, how will you connect the resistances? b) In both circumstances, calculate the strength of the total current in the circuit.

answer: a) When the two resistors are linked in series, the current through the resistors is kept to a minimum. The current flow is greatest when the resistors are linked in parallel. b) If 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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The potential difference across a lamp is 12V. How many joules of electrical energy are changed into heat and light when: a) a charge of 1C passes through it? b) a charge of 5C passes through it? c) a current of 2A flows through it for 10s?

Given, Potential difference $=12 \mathrm{~V}$ a) Potential difference = (work done)/(charge moved) Work done = Potential difference$\times$ charge moved Therefore, $12 \mathrm{~J}$ of electrical...

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What is a circuit diagram? Draw the labelled diagram of an electric circuit comprising of a cell, a resistor, an ammeter, a voltmeter, and a closed switch or closed plug key. Which of the two has a large resistance: an ammeter or a voltmeter?

A circuit diagram is a graphic that uses electric symbols to show the individual components in an electric circuit and how they are connected. A voltmeter, on the other hand, will have a higher...

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Q16. a) Give two examples of substances which are good conductors of electricity. Why do you think they are good conductors of electricity? b) Calculate the resistance of a copper wire 1.0km long and 0.50mm diameter if the resistivity of copper is 1.7×10-8Ωm.

Answer: a) Two examples of substances that are good conductors of electricity are silver and copper. These two metals have free electrons that are available for conduction. b) Given in question : l...

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A 6V battery is linked in series with a 20 resistance electric bulb and a 4 resistance cable. Create a circuit schematic and perform the following calculations: c) potential difference between the electric bulb and the resistance wire d) potential difference between the electric bulb and the resistance wire

Answer: c) Difference in potential across the bulb = IR1 = 0.25 20 = 5V d) Difference in potential across the resistance wire = IR2 = 0.25 4 = 1V

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Q15. a) Write down an expression for the resistance of a metallic wire in terms of the resistivity. b) What will be the resistance of a metal wire of length 2 metres and area of cross-section 1.55×10-6m2, if the resistivity of the metal be 2.8×10-8Ωm?

Answer: a) Following is the expression for the resistance of a metallic wire in terms of the resistivity: R = ρl/A Where, R is the resistance of the wire , ρ is the resistivity of the wire , A is...

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c) An electrician has wired a house in such a way that if a lamp gets fused in one room of the house, all the lamps in other rooms of the house stop working. What is the defect in the wiring? d) Draw a circuit diagram showing two electric lamps connected in parallel together with a cell and a switch that works both lamps. Mark an A enclosed in a circle on your diagram to show where an ammeter should be placed to measure the current.

Answer: c) All of the lamps are linked together in a series combination. d)

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Ten bulbs are connected in a series circuit to a power supply line. Ten identical bulbs are connected in a: a) an identical power supply line b) which circuit would have the highest voltage across each bulb? c) in which circuit would the bulbs be brighter? d) in which circuit, if one bulb blows out, all others will stop glowing? e) which circuit would have less current in it?

Answer: The following are the right answers: c) When a parallel circuit is employed, the appliance's operation can be regulated by individual switches. d) When appliances are linked in parallel,...

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Ten bulbs are connected in a series circuit to a power supply line. Ten identical bulbs are connected in a: a) an identical power supply line b) which circuit would have the highest voltage across each bulb? c) in which circuit would the bulbs be brighter? d) in which circuit, if one bulb blows out, all others will stop glowing? e) which circuit would have less current in it?

Answer: The following are the correct answers: a) The circuit must be parallel to have an identical power supply line. b) Each bulb will have the highest voltage when the circuit is parallel.

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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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