$A$ simple pendulum of length $1 \ m$ has a bob of mass $1 \ kg$. $A$ bullet of mass $10^{-2} \ kg$ is fired into the bob with a speed of $2 \times 10^2 \ m/s$. The bullet gets embedded in the bob. Find the height $h$ to which the bob rises before it swings back. (in $m$)

$A$ body of mass $0.5 \ kg$ is supplied with a power $P$ (in watt) which varies with time $t$ (in second) as $P = 3t^2 + 3$. If the velocity of the body at time $t = 0$ is zero, then the velocity of the body at time $t = 3 \ s$ is (in $ms^{-1}$)

$A$ body of mass $10 \, kg$ at rest is acted upon simultaneously by two forces $4 \, N$ and $3 \, N$ at right angles to each other. The kinetic energy of the body at the end of $10 \, s$ is .............. $J$.

$A$ ball of mass $1 \ kg$ moving with a velocity of $0.4 \ m/s$ collides with another ball of the same mass at rest. After the collision,the first ball moves with a velocity of $0.3 \ m/s$ in a direction perpendicular to the initial direction. Find the magnitude of the momentum $\vec{P}$ of the second ball in $kg \cdot m/s$.

$A$ bullet of mass $0.02 \ kg$ travelling horizontally with velocity $250 \ ms^{-1}$ strikes a block of wood of mass $0.23 \ kg$ which rests on a rough horizontal surface. After the impact,the block and bullet move together and come to rest after travelling a distance of $40 \ m$. The coefficient of sliding friction of the rough surface is $\left(g=9.8 \ ms^{-2}\right)$

$A$ particle of mass $m$ moving eastward with a speed $v$ collides with another particle of same mass moving northward with same speed $v$. The two particles coalesce after collision. The new particle of mass $2m$ will move in north-east direction with a speed (in $m/s$) of: