$A$ body of mass $2 \, kg$ slides down a curved track which is a quadrant of a circle of radius $1 \, m$ as shown in the figure. All the surfaces are frictionless. If the body starts from rest,its speed at the bottom of the track is ............. $m/s$.

The rain drop of mass $1 \text{ g}$,starts with zero velocity from a height of $1 \text{ km}$. It hits the ground with a speed of $5 \text{ m/s}$. The work done by the unknown resistive force is . . . . . . $J$. (take $g = 10 \text{ m/s}^2$)

$A$ ball bounces to $80\%$ of its original height. What fraction of its mechanical energy is lost in each bounce?

What can be said about the law of conservation of energy?

$A$ pendulum bob has a speed $4 \,m/s$ at its lowest position. The pendulum is $1 \,m$ long. When the length of the string makes an angle of $60^{\circ}$ with the vertical, the speed of the bob at that position is (acceleration due to gravity, $g=10 \,m/s^2, \cos 60^{\circ}=0.5$).

$A$ block weighing $20 \ N$ travels down a smooth curved track $AB$ joined to a rough horizontal surface (figure). The rough surface has a friction coefficient of $0.40$ with the block. If the block starts slipping on the track from a point $1.0 \ m$ above the horizontal surface,the distance it will move on the rough surface is: (in $m$)