An object falls from a height of $20 \ cm$ on the surface of the Earth. If $75\%$ of its mechanical energy is lost after striking the Earth,the object will rebound to a height of ......... $cm$.

$A$ water pump is driven by a petrol engine that pumps water from a depth of $30 \ m$ at a rate of $0.5 \ m^3/min$. If the efficiency of the pump is $70\%$, what is the power generated by the engine in $W$?

In the case of circular motion of a body,if a tangential force also acts on the body in addition to a centripetal force,then the work done:

Two bodies of different masses $m_1$ and $m_2$ have equal momenta. Their kinetic energies $E_1$ and $E_2$ are in the ratio:

$A$ force exerts an impulse $I$ on a particle changing its speed from $u$ to $2u$. The applied force and the initial velocity are oppositely directed along the same line. The work done by the force is

Two identical blocks $A$ and $B$,each of mass $m$,resting on a smooth floor,are connected by a light spring of natural length $L$ and spring constant $K$. The spring is at its natural length. $A$ third identical block $C$ (mass $m$) moving with a speed $v$ along the line joining $A$ and $B$ collides with $A$. The maximum compression in the spring is: