The force $F$ acting on a body moving in a circle of radius $r$ is always perpendicular to  the instantaneous velocity $v$. The work done by the force on the body in one complete  rotation is : 

Power applied to a particle varies with time as $P = [3t^2 -2t + 1]$ $watt$ then the change in kinetic energy of particle from $t = 2\,sec$ to $t = 4\,sec.$ ............... $\mathrm{J}$

A particle of mass $M$ starting from rest undergoes uniform acceleration. If the speed acquired in time $T$ is $V$, then power delivered to the particle in time $T$ is

A disc of mass $M$ and radius $R$ rolls on a horizontal surface and then rolls up an inclined plane as shown in the figure. If the velocity of the disc is $v$, the height to which the disc will rise will be

A force $F$ acting on an object varies with distance $x$ as shown in the figure. The work done by the force in moving the object from $x = 0$ to $x = 8\,m$ is  ......... $J$

A ball after falling from a height of $10\, m$ strikes the roof of a lift which is descending  down with a velocity of $1\, m/s$. The recoil velocity of the ball will be .............. $\mathrm{m}/ \mathrm{s}$