Question 1 :
The kinetic energy of particle moving along a circle of radius R depends upon the distance covered S and is given by {tex}K = aS^2{/tex} where a is a constant. Then the force acting on the particle is

Question 2 :
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

Question 3 :
The power required to keep the belt moving is ____ $\dfrac{d}{dt}$ (KE)

Question 4 :
In elastic collision, {tex} 100 \% {/tex} energy transfer takes place when

Question 5 :
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 6 :
If a shell fired from a cannon, explodes in mid air, then

Question 7 :
A body of mass {tex} 1 \mathrm { kg } {/tex} begins to move under the action of a time dependent force {tex} \vec { \mathrm { F } } = \left( 2 \mathrm { t } \hat { \mathrm { i } } + 3 \mathrm { t } ^ { 2 } \hat { \mathrm { j } } \right) \mathrm { N } {/tex} where {tex} \hat { \mathrm { i } } {/tex} and {tex} \hat { \mathrm { j } } {/tex} are unit vectors along {tex} \mathrm { x } {/tex} and {tex} \mathrm { y } {/tex} axis. What power will be developed by the force at the time {tex} \mathrm {t} {/tex} ?

Question 8 :
A vehicle is moving with a uniform velocity on a smooth horizontal road, then power delivered by its engine must be

Question 9 :
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 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 :
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 12 :
A man of weight $50\&#160; kg$ carries an object&#160;to a height of $20\ m$ in a time of $10\&#160; s$. The power used by the man in the this&#160;process is $2000\ W$, then find the mass of the object carried by the man.<br/>[assume&#160;$g= 10 ms^{-2}]$

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 body is acted upon by a force $ F = \hat{i} + 2 \hat{j} + 3 \hat{k} $ . The work done by the force in displacing it from $ (0, 0, 0) $ to $ (0,0,4m)$ will be -

Question 16 :
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 17 :
A force F = – K (yi + xj) (where K is a positive constant) acts on a particle moving in the xy-plane. Starting from the origin, the particle is taken along the positive x-axis to the point (a, 0) and then parallel to the y-axis to the point (a, a). The total work done by the force F on the particles is

Question 18 :
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 19 :
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 20 :
Two blocks of masses {tex} m{/tex} and {tex}M{/tex} are joined with an ideal spring of spring constant {tex}k{/tex} and kept on a rough surface as shown. The spring is initially unstretched and the coefficient of friction between the blocks and the horizontal surface is {tex} \mu . {/tex} What should be the maximum speed of the block of mass {tex} M {/tex} such that the smaller block does not move?<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NEET/5e0ee764dc973f528b538d04">