$A$ bob of a pendulum of length $0.5 \ m$ has a speed of $6 \ ms^{-1}$ at its lowest point. Find the speed of the bob when the string of the pendulum makes $60^{\circ}$ with the vertical. (Take $g=10 \ ms^{-2}$)

$A$ 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 $\,m$)

$A$ car comes to rest after traveling a distance $s$ under a constant retarding force $F$. If the mass of the car is increased by $50\%$,at what distance will the car come to rest,assuming the same retarding force $F$ and initial velocity $v$?

$A$ bullet is fired at a target with velocity $V$. Its velocity decreases from $V$ to $V/2$ when it penetrates $30 \ cm$ into the target. Through what additional thickness will it penetrate further into the target before coming to rest (in $cm$)?

$A$ bullet of mass $20\,g$ has an initial speed of $1\,ms^{-1}$ just before it starts penetrating a mud wall of thickness $20\,cm.$ If the wall offers a mean resistance of $2.5 \times 10^{-2}\,N,$ the speed of the bullet after emerging from the other side of the wall is close to .............. $ms^{-1}$

$A$ bus moving on a level road with a velocity $v$ can be stopped at a distance of $x$ by the application of a retarding force $F$. The load on the bus is increased by $25\%$ by boarding the passengers. Now, if the bus is moving with the same speed and if the same retarding force is applied, the distance travelled by the bus before it stops is