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Q 1. The displacement-time graph of particle is shown in Fig. 4.17 .

Work done by all the forces in part {tex} O A {/tex} is greater than zero

Work done by all the forces in part {tex} A B {/tex} is greater than zero

Work done by all the forces in part {tex} B C {/tex} is greater than zero

Work done by all the forces in part {tex} A B {/tex} is less than zero

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Q 2. A small block of mass {tex} 0.1 \mathrm { kg } {/tex} is pressed against a horizontal spring fixed at one end to compress the spring through {tex} 5.0\mathrm { cm } {/tex} as shown in below Fig. The spring constant is {tex}100 \mathrm { Nm } {/tex} . When released the block moves horizontally till it leaves the spring, it will hit the ground {tex}2 \mathrm { m } {/tex} below the spring.

At a horizontal distance of {tex} 1 \mathrm { m } {/tex} from free end of the spring.

At a horizontal distance of {tex}2 \mathrm { m } {/tex} from free end of the spring.

Vertically below the edge on which the mass is resting.

At a horizontal distance of {tex} \sqrt { 2 } \mathrm { m } {/tex} from free end of the spring.

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Q 3. A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle. The motion of the particle takes place in a plane. It follows that

Its velocity is constant.

Its acceleration is constant.

Its kinetic energy is constant.

It moves in a straight line.

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Q 4. Two identical balls are projected, one vertically up and the other at an angle of with {tex}\mathrm{30^\circ}{/tex} the horizontal, with same initial speed. The potential energy at the highest point is in the ratio

{tex} 4 : 3 {/tex}

{tex} 3 : 4 {/tex}

{tex} 4 : 1 {/tex}

{tex} 1 : 4 {/tex}

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Q 5. The unit of power is

Kilowatt

Kilowatt-hour

Dyne

Joule

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Q 6. A particle projected with an initial velocity {tex} u {/tex} at angle {tex} \theta {/tex} from the ground. The work done by gravity during the time it reaches the highest point {tex} P {/tex} is:

{tex} \frac { - m u ^ { 2 } \sin ^ { 2 } \theta } { 2 } {/tex}

{tex} + \frac { m u ^ { 2 } \sin ^ { 2 } \theta } { 2 } {/tex}

0

{tex} + m u ^ { 2 } \sin \theta {/tex}

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Q 7. A block of mass {tex} m {/tex} is slowly pulled up on inclined plane of height {tex} h {/tex} and inclination {tex} \theta {/tex} with the top of a string parallel to the incline. Which of the following statement is correct for the block when it moves up from the bottom to the top of the incline?

Work done by the normal reaction force is zero.

Work done by the string on block is {tex} { mgh } {/tex} .

Work done by the gravity is {tex} m g h {/tex}

Work done by the block is {tex} - m g h / 2 {/tex}

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Q 8. A block of mass {tex}2 \mathrm {kg}{/tex} is lifeted through a chain. When block moves through {tex}2 \mathrm {m}{/tex} vertically the velocity becomes {tex} 4 \mathrm { m } / \mathrm { s } . {/tex} Work done by chain force until it moves {tex}2 \mathrm { m } {/tex} is {tex} \left( g = 10 \mathrm { ms } ^ { - 2 } \right) {/tex}

{tex} 40\mathrm { J } {/tex}

{tex}24 \mathrm { J } {/tex}

{tex}56 \mathrm { J } {/tex}

None of these

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Q 9. A position-dependent force {tex} F = 7 - 2 x + 3 x ^ { 2 } N {/tex} acts on a small body of mass {tex}2 \mathrm { kg } {/tex} and displaces it from {tex} x = 0 {/tex} to {tex} x = 5 \mathrm { m } . {/tex} The work done in joule is

{tex}70 \mathrm { J } {/tex}

{tex} 270\mathrm { J } {/tex}

{tex}35\mathrm { J } {/tex}

{tex}135\mathrm { J } {/tex}

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Q 10. A particle is released from rest at origin. It moves under the influence of potential field {tex} U = x ^ { 2 } - 3 x {/tex} where {tex} U {/tex} is in Joule and {tex} x {/tex} is in metre. Kinetic energy at {tex} x = 2 \mathrm { m } {/tex} will be

{tex}2 \mathrm { J } {/tex}

{tex}1 \mathrm { J } {/tex}

{tex} 1.5\mathrm { J } {/tex}

{tex}0 \mathrm { J } {/tex}

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Q 11. The potential energy of a particle of mass {tex} m {/tex} is given by {tex} U = \frac { 1 } { 2 } k x ^ { 2 } {/tex} for {tex} x < 0 {/tex} and {tex} U = 0 {/tex} for {tex} x \geq 0 . {/tex} If total mechanical energy of the particle is {tex} E . {/tex} Then its speed at {tex} x = \sqrt { \frac { 2 E } { k } } {/tex} is

Zero

{tex} \sqrt { \frac { 2 E } { m } } {/tex}

{tex} \sqrt { \frac { E } { m } } {/tex}

{tex} \sqrt { \frac { E } { 2 m } } {/tex}

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Q 12. A cricket ball is hit for a six leaving the bat at an angle of {tex} 45 ^ { \circ } {/tex} to the horizontal with kinetic energy {tex} K . {/tex} At the top position, the kinetic energy of the ball is

Zero

{tex} K {/tex}

{tex} K / 2 {/tex}

{tex} K / \sqrt { 2 } {/tex}

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Q 13. A bullet losses {tex}19 \% {/tex} of its kinetic energy when passes through an obstacle. The percentage change in its speed is

Reduced by {tex} 10\% {/tex}

Reduced by {tex} 19\% {/tex}

Reduced by {tex}9.5 \% {/tex}

Reduced by {tex} 11\% {/tex}

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Q 14. Two springs {tex} A {/tex} and {tex} B \left( k _ { A } = 2 k _ { B } \right) {/tex} are stretched by applying forces of equal magnitudes at the ends. If the energy stored in {tex} A {/tex} is {tex} E {/tex} , then energy stored in {tex} B {/tex} is

{tex} \frac { E } { 2 } {/tex}

{tex}2 E {/tex}

{tex} E {/tex}

{tex} \frac { E } { 4 } {/tex}

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Q 15. A particle of mass {tex}2 \mathrm { kg } {/tex} starts moving in a straight line with an initial velocity of {tex} 2\mathrm { m } / \mathrm { s } {/tex} at a constant acceleration of {tex} 2 \mathrm { m } / \mathrm { s } ^ { 2 } . {/tex} The rate of change of kinetic energy is

Four times the velocity at any moment.

Two times the displacement at any moment.

Four times the rate of change of velocity at any moment.

Constant throughout.

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Q 16. A block of mass {tex} m = 0.1 \mathrm { kg } {/tex} is released from a height of {tex}4 \mathrm { m } {/tex} on a curved smooth surface. On the horizontal smooth surface, it collides with a spring of force constant {tex} 800\mathrm { N } / \mathrm { m } {/tex} . The maximum compression in spring will be {tex} \left( g = 10 \mathrm { m } / \mathrm { s } ^ { 2 } \right) {/tex}

{tex} 1\mathrm { cm } {/tex}

{tex}5 \mathrm { cm } {/tex}

{tex}10 \mathrm { cm } {/tex}

{tex}20 \mathrm { cm } {/tex}

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Q 17. An ideal spring with spring-constant {tex} k {/tex} is hung from the ceiling and a block of mass {tex} m {/tex} is attached to its lower end. The mass is released with the spring initially unstretched. Then the maximum extension in the spring is

{tex} \frac { 4 m g } { k } {/tex}

{tex} \frac { 2 m g } { k } {/tex}

{tex} \frac { m g } { k } {/tex}

{tex} \frac { m g } { 2 k } {/tex}

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Q 18. A variable force {tex}\mathrm F{/tex} starts acting on a block of mass {tex} 5{ kg } {/tex} resting on a smooth horizontal surface. {tex}\mathrm F{/tex} is varying with displacement {tex} x {/tex} as shown in {tex} F - x {/tex} curve. The velocity of body when its displacement is {tex}3 { m } {/tex} will be

{tex}2 \ \mathrm { ms } ^ { - 1 } {/tex}

{tex}2 \sqrt { 2 } \mathrm { ms } ^ { - 1 } {/tex}

{tex} 2 \sqrt { 3 } \mathrm { ms } ^ { - 1 } {/tex}

{tex}6\ \mathrm { ms } ^ { - 1 } {/tex}

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Q 19. When a body moves in a circle, the work done by the centripetal force is always

{tex} > 0 {/tex}

{tex} < 0 {/tex}

Zero

None of these

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Q 20. A block of mass {tex} 2\mathrm { kg } {/tex} is held over a vertical spring free with spring unstretched. Suddenly, if block is left free, maximum compression of spring is [spring constant {tex} K = 200 \mathrm { N } / \mathrm { m } ] {/tex} :

{tex} 0.2\mathrm { m } {/tex}

{tex} 0.1\mathrm { m } {/tex}

{tex} 0.4\mathrm { m } {/tex}

{tex}0.05 \mathrm { m } {/tex}

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Q 21. A small block of mass 0.1 kg is pressed against a horizontal spring fixed at one end to compress the spring through 5.0 cm as shown. The spring constant is

100 N/m. When released the block moves horizontally till it leaves the spring. It will hit the ground 2 m below the spring.

at a horizontal distance of 1 m from free end of the spring

at a horizontal distance of 2 m from free end of the spring

vertically below the edge on which the mass is resting

at a horizontal distance of {tex}\sqrt{2}{/tex} m from free end of the spring.

{tex}\frac{1}{2}(\text{100})\left( \frac{5}{\text{100}} \right)^{2} = \frac{1}{2}\text{mv}^{2} \Rightarrow \ v = \sqrt{\frac{5}{2}}{/tex}; {tex}x = v\sqrt{\frac{2h}{g}} = 1\text{\ m}{/tex}

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Q 22. A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle. The motion of the particle takes place in a plane. It follows that

its velocity is constant

its acceleration is constant

its kinetic energy is constant

it moves in a straight line

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Q 23. Two identical balls are projected, one vertically up and the other at an angle of 30° with the horizontal, with same initial speed. The potential energy at the highest point is in the ratio

4 : 3

3 : 4

4 : 1

1 : 4

{tex}h_{1} = \frac{u^{2}}{2g},\ h_{2} = \frac{(u\text{sin}\text{30}{^\circ})^{2}}{2g} = \frac{u^{2}}{8g}{/tex}

*h*_{1} : *h*_{2} = 4 : 1

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Q 24. The unit of power is

kilowatt

kilowatt-hour

dyne

joule

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Q 25. A particle of mass *m* is projected with an initial velocity *u* at angle θ from the ground. What is the work done by gravity during the time it reaches the highest point *P* is:

{tex}\frac{- \text{mu}^{2}\text{sin}^{2}\theta}{2}{/tex}

{tex}+ \frac{\text{mu}^{2}\text{sin}^{2}\theta}{2}{/tex}

0

+ mu^{2}sin*θ*

Work done =− mgH_{max} = {tex}- \text{mg}\frac{u^{2}\text{sin}^{2}\theta}{2g}{/tex} = {tex}\frac{- \text{mu}^{2}\text{sin}^{2}\theta}{2}{/tex}

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