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 ......... $cm$.

To maintain a speed of $80\,km/h$ by a bus of mass $500\,kg$ on a plane rough road for $4\,km$ distance,the work done by the engine of the bus will be $........\,kJ$. [The coefficient of friction between the tyre of the bus and the road is $0.04$].

$A$ particle of mass $m$ moving with velocity $V_0$ strikes a simple pendulum of mass $m$ and sticks to it. The maximum height attained by the pendulum will be

In two separate collisions,the coefficients of restitution $e_1$ and $e_2$ are in the ratio $3: 1$. In the first collision,the relative velocity of approach is twice the relative velocity of separation. Then,the ratio between the relative velocity of approach and the relative velocity of separation in the second collision is:

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:

The sign of work done by a force on a body is important to understand. State carefully if the following quantities are positive or negative:
$(a)$ Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket.
$(b)$ Work done by gravitational force in the above case.
$(c)$ Work done by friction on a body sliding down an inclined plane.
$(d)$ Work done by an applied force on a body moving on a rough horizontal plane with uniform velocity.
$(e)$ Work done by the resistive force of air on a vibrating pendulum in bringing it to rest.