Consider a drop of rain water having mass $1\,g$ falling from a height of $1\,km$. It hits the ground with a speed of $50\,m s^{-1}$. Take $g = 10\,m s^{-2}$. The work done by the $(i)$ gravitational force and the $(ii)$ resistive force of air is

$A$ bullet of mass $m_1$ is moving with speed $v_0$ and hits a sand bag of mass $m_2$. If the speed of the bullet after passing through the sand bag is $\frac{v_0}{3}$,then the height $h$ up to which the bag rises is (assume,$g=$ acceleration due to gravity).

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:

$A$ baseball having mass of $0.4 \ kg$ is thrown such that one of the forces acting on it varies with time as shown in the first graph. Also,the velocity of the ball is in the same direction as the force. The velocity varies with time as shown in the second graph. Choose the incorrect option (up to $0.3 \ s$).

Two blocks of masses $m_1$ and $m_2$ are connected by a spring of spring constant $k$,initially at their natural length as shown. $A$ sharp impulse is given to mass $m_2$ so that it acquires a velocity $v_0$ towards the right. If the system is kept on a smooth floor,find the maximum elongation that the spring will suffer.

$A$ raindrop of mass $1.00 \, g$ falling from a height of $1 \, km$ hits the ground with a speed of $50 \, m s^{-1}$. Calculate
$(a)$ the loss of $PE$ of the drop
$(b)$ the gain in $KE$ of the drop
$(c)$ Is the gain in $KE$ equal to loss of $PE$? If not,why?
Take $g = 10 \, m s^{-2}$.