$A$ mass of $10 \, g$ moving with a velocity of $100 \, cm/s$ strikes a pendulum bob of mass $10 \, g$. The two masses stick together. The maximum height reached by the system now is ............... $cm$ $(g = 10 \, m/s^2)$.

$A$ target is made of two plates,one of wood and the other of iron. The thickness of the wooden plate is $4\,cm$ and that of the iron plate is $2\,cm$. $A$ bullet fired goes through the wood first and then penetrates $1\,cm$ into the iron. $A$ similar bullet fired with the same velocity from the opposite direction goes through the iron first and then penetrates $2\,cm$ into the wood. If $a_1$ and $a_2$ are the retardations offered to the bullet by the wood and iron plates respectively,then:

$A$ ball of mass $m$ falls vertically to the ground from a height $h_1$ and rebounds to a height $h_2$. The change in momentum of the ball on striking the ground is

$A$ bob $B$ of mass $m$ at rest is hanging vertically from the ceiling via a massless string of length $10 \text{ m}$. $A$ point mass $A$ of mass $m$ travelling horizontally with speed $10 \text{ ms}^{-1}$ hits bob $B$ elastically. The bob $B$ rises $h$ meters after the collision. Taking the acceleration due to gravity $g = 10 \text{ ms}^{-2}$ and neglecting the size of the bob, the value of $h$ is:

$A$ particle is moving in a circle of radius $r$ under the action of a force $F = \alpha r^2$ which is directed towards the centre of the circle. The total mechanical energy (kinetic energy + potential energy) of the particle is (take potential energy $= 0$ for $r = 0$).

$A$ lorry and a car moving with the same $K.E.$ are brought to rest by applying the same retarding force,then