$A$ body moving with velocity $v$ has momentum and kinetic energy numerically equal. What is the value of $v$ in $m/s$?

$300 \, J$ of work is done in sliding up a $2 \, kg$ block on an inclined plane to a height of $10 \, m$. Taking the value of acceleration due to gravity $g$ to be $10 \, m/s^2$,the work done against friction is ........ $J$.

$A$ $0.5 \, kg$ block moving at a speed of $12 \, ms^{-1}$ compresses a spring through a distance of $30 \, cm$ when its speed is halved. The spring constant of the spring in $N m^{-1}$ is:

Two balls at the same temperature collide. What is conserved?

It is well known that a raindrop falls under the influence of the downward gravitational force and the opposing resistive force. The latter is known to be proportional to the speed of the drop but is otherwise undetermined. Consider a drop of mass $1.00 \; g$ falling from a height $1.00 \; km$. It hits the ground with a speed of $50.0 \; m s^{-1}$. $(a)$ What is the work done by the gravitational force? $(b)$ What is the work done by the unknown resistive force?

$A$ large block of wood of mass $M = 5.99 \, kg$ is hanging from two long massless cords. $A$ bullet of mass $m = 10 \, g$ is fired into the block and gets embedded in it. The (block $+$ bullet) then swing upwards,their centre of mass rising a vertical distance $h = 9.8 \, cm$ before the (block $+$ bullet) pendulum comes momentarily to rest at the end of its arc. The speed of the bullet just before collision is: (Take $g = 9.8 \, ms^{-2}$) (in $m/s$)