$A$ 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:

$A$ particle is released from a height $H$. At a certain height $h$,its kinetic energy is two times its potential energy. The height $h$ and the speed $v$ of the particle at that instant are:

An object of mass $20 \,kg$ is displaced by $x = 5t^2 \,m$ (where $t$ is time) due to the application of a force. The ratio of the work done in $3 \,s$ and $5 \,s$ is:

$A$ body of mass $m$ starts moving from rest along the $x-$axis such that its velocity varies as $v = a\sqrt{s}$,where $a$ is a constant and $s$ is the distance covered by the body. The total work done by all the forces acting on the body in the first $t$ seconds after the start of the motion is:

$A$ 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 $m$)

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