Question 1 :
In elastic collision, {tex} 100 \% {/tex} energy transfer takes place when

Question 2 :
One man takes {tex} 1 \mathrm { min } {/tex}. to raise a box to a height of {tex}1{/tex} metre and another man takes {tex} 1 / 2 \mathrm { min } {/tex}. to do so. The energy of the

Question 3 :
Two blocks of masses {tex} m _ { 1 } = 10 \mathrm { kg } {/tex} and {tex} m _ { 2 } = 20 \mathrm { kg } {/tex} are connected by a spring of stiffness {tex} k = 200 \mathrm { N } / \mathrm { s } {/tex} {tex} \mathrm { m } {/tex}. The coefficient of friction between the blocks and the fixed horizontal surface is {tex} \mu = 0.1 . {/tex} Find the minimum constant horizontal force {tex} F {/tex} (in newtons) to be applied to {tex} \mathrm { m } _ { 1 } {/tex} in order to slide the mass {tex} m _ { 2 } . {/tex} <br> [Take {tex} \mathrm {g= 10 m/s ^2}{/tex}

Question 4 :
A particle is taken round a circle by application of force. The work done by the force is

Question 5 :
A <b>10 m</b> long iron chain of linear mass density <b>0.8 kgm^-1</b> is hanging freely from a rigid support. If <b>g = 10 ms^-2</b>, then the power required to left the chain upto the point of support in 10 second

Question 6 :
A bomb of mass {tex}9 \mathrm{kg}{/tex} explodes into the pieces of masses {tex} 3 \mathrm { kg } {/tex} and {tex} 6 \mathrm { kg } {/tex}. The velocity of mass {tex} 3 \mathrm { kg } {/tex} is {tex} 16 \mathrm { m } / \mathrm { s } {/tex}. The kinetic energy of mass {tex} 6 \mathrm { kg } {/tex} in joule is

Question 8 :
A {tex}10{/tex} H.P. motor pumps out water from a well of depth {tex} 20 \mathrm { m } {/tex} and fills a water tank of volume {tex}22380{/tex} litres at a height of {tex}10 \mathrm { m } {/tex} from the ground. The running time of the motor to fill the empty water tank is {tex} \left( \mathrm { g } = 10 \mathrm { ms } ^ { - 2 } \right) {/tex}

Question 9 :
If a shell fired from a cannon, explodes in mid air, then

Question 10 :
A block of mass {tex} 0.50 \mathrm { kg } {/tex} is moving with a speed of {tex} 2.00\ \mathrm { ms } ^ { - 1 } {/tex} on a smooth surface. It strikes another mass of {tex} 1.00 \ \mathrm { kg } {/tex} and then they move together as a single body. The energy loss during the collision is

Question 11 :
If the momentum of a body is increased by <b>50%</b> then the percentage increase in its kinetic energy is

Question 12 :
The work done on a particle of mass $m$ by a force $K \left[\dfrac{x}{(x<br>^{2}+y^{2})^{3/2}}\hat{i}+\dfrac{y}{(x^{2}+y^{2})^{3/2}}\hat{j} \right] $, where $K$ being a constant of appropriate dimensions, when the particle is taken from the point $(a,\ 0)$to the point $(0,\ a)$along a circular path of radius $a$ about the origin in the x-y plane is:<br>

Question 13 :
How much water, a pump of {tex} 2 \mathrm { kW } {/tex} can raise in one minute to a height of {tex} 10 \mathrm { m } , {/tex} take {tex} \mathrm { g } = 10 \mathrm { m } / \mathrm { s } ^ { 2 } ? {/tex}

Question 14 :
A vehicle is moving with a uniform velocity on a smooth horizontal road, then power delivered by its engine must be

Question 15 :
A body of mass {tex} 0.5 \mathrm { kg } {/tex} travels in a straight line with velocity {tex} v = 5 x ^ { 3 / 2 } . {/tex} The work done by the net force during the displacement from {tex} x = 0 {/tex} to {tex} x = 2 \mathrm { m } {/tex} is

Question 16 :
An object of mass <b>2kg </b> makes an elastic collision with another object of mass <b> M </b> at rest and continues to move in the original direction but with one-fourth of its original speed. What is the value of <b>M </b>?

Question 17 :
A car of mass {tex} m {/tex} starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude {tex} p _ { 0 } {/tex}. The instantaneous velocity of this car is proportiourl to:

Question 18 :
In an inelastic collision, which of the following does not remain conserved?

Question 19 :
According to work-energy theorem, the work done by the net force on a particle is equal to the change in its

Question 20 :
The coefficient of restitution e for a perfectly elastic collision is

Question 21 :
Two bodies {tex} A {/tex} and {tex} B {/tex} having masses in the ratio of 3: 1 possess the same kinetic energy. The ratio of linear momentum of {tex} B {/tex} to {tex} A {/tex} is

Question 22 :
If W represents the work done, then match the two columns:<br><table> <tr><th>Column I </th> <th>Column II</th> </tr> <tr><td>(A)Force is always along the velocity</td> <td>(1)W=0</td> </tr> <tr><td>(B)Force is always perpendicular to velocity </td> <td>(2)W<0</td> </tr> <tr><td>(C)Force is always perpendicular to acceleration</td> <td>(3)W>0</td> </tr> <tr><td>(D)The object is stationary but the point of application of the force moves on the object</td> <td></td> </tr> </table>

Question 23 :
Calculate the work done on the tool by {tex} \vec { F } {/tex} if this displacement is along the straight line {tex} y = x {/tex} that connects these two points.

Question 24 :
A force {tex} F = - K ( y \hat { i } + x \hat { j } ) {/tex} (where {tex} K {/tex} is a positive constant) acts on a particle moving in the {tex} x y {/tex} plane. Starting from the origin, the particle is taken along the positive {tex} x {/tex} axis to the point {tex} ( a , 0 ) , {/tex} and then parallel to the {tex} y {/tex} axis to the point {tex} ( a , a ) , {/tex} The total work done by the force {tex} F {/tex} on the particle is

Question 25 :
A spherical ball of mass {tex} 20 \mathrm { kg } {/tex} is stationary at the top of a hill of height {tex} 100 \mathrm { m } {/tex}. It rolls down a smooth surface to the ground, then climbs up another hill of height {tex} 30 \mathrm { m } {/tex} and finally rolls down to a horizontal base at a height of {tex} 20 \mathrm { m } {/tex} above the ground. The velocity attained by the ball is

Question 26 :
A mass of {tex} 20 \mathrm { kg } {/tex} moving with a speed of {tex} 10 \mathrm { m } / \mathrm { s } {/tex} collides with another stationary mass of {tex} 5 \mathrm { kg } {/tex}. As a result of the collision, the two masses stick together. The kinetic energy of the composite mass will be

Question 27 :
A vehicle of mass $M$ is accelerated on a horizontal frictionless road under a force changing its velocity from $u$ to $v$ and distance covered is $S$. A constant power $P $ is given by the engine of the vehicle. The $v$ is equal to

Question 28 :
A body is moved along a straight line by a machine delivering constant power. The distance moved by the body in time t is proportional to

Question 29 :
A bullet is fired and gets embedded in block kept on table. If table is frictionless, then

Question 30 :
Johnny and his sister Jane race up a hill. Johnny weighs twice as much as jane and takes twice as long as jane to reach the top. Compared to Jane