$A$ child is swinging on a swing. The minimum and maximum heights of the swing from the earth's surface are $0.75\,m$ and $2\,m$ respectively. The maximum velocity of this swing is ............. $m/s$.

In the presence of which of the following is the work-energy theorem valid?

$A$ body of mass $m$ slides down a smooth hemispherical surface of radius $r$. What will be its velocity at the bottom of the surface?

$A$ bullet of mass $10 \; g$ leaves a rifle at an initial velocity of $1000 \; m/s$ and strikes the earth at the same level with a velocity of $500 \; m/s$. The work done in joule $(J)$ in overcoming the resistance of air will be:

What does the law of conservation of energy state?

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 $\,m$)