$A$ pendulum bob has a speed of $3 \, m/s$ at its lowest position. The pendulum is $50 \, cm$ long. The speed of the bob, when the string makes an angle of $60^{\circ}$ to the vertical, will be $....... \, m/s$ $(g = 10 \, m/s^2)$.

Two monkeys with the same mass stand on a branch at height $h$ above the horizontal jungle floor. Monkey $A$ steps off the branch holding the end of an inextensible rope of length $L$ whose other end is tied to another branch at height $H$,lets go at the bottom of the swing,and falls freely to the floor,as shown below. Monkey $B$ steps off and falls straight downward. Then,neglecting air resistance but not the tension in the rope,the total work $W$ done on each monkey and the speed $v$ with which each hits the floor are as follows:

$A$ bullet of mass $m$ enters a wooden block of length $L$ at a speed $v_1$ and emerges out of the block with a speed $v_2$. If $F$ is the average force which impeded its motion through the wooden block, then (Assume uniform deceleration inside the block):

$A$ simple pendulum is released from point $A$ as shown in the figure. If $m$ and $l$ represent the mass of the bob and the length of the pendulum respectively,the gain in kinetic energy at point $B$ is:

From a height of $h$ above the ground, a ball is projected up at an angle $30^{\circ}$ with the horizontal. If the ball strikes the ground with a speed of $1.25$ times its initial speed of $40 \,ms^{-1}$, the value of $h$ is (acceleration due to gravity $= 10 \,ms^{-2}$) (in $\,m$)

$A$ ball at rest is dropped from a height of $12 \,m$. It loses $25 \%$ of its kinetic energy on striking the ground and bounces back to a height '$h$'. Then the value of '$h$' is (in $\,m$)