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

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.

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

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

Q 5. The unit of power is

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:

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?

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}

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

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

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

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

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

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

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

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}

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

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

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

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} :

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.

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

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

Q 24. The unit of power is

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: