$A$ uniform flexible chain of mass $m$ and length $2l$ hangs in equilibrium over a smooth horizontal pin of negligible diameter. What will be the speed of the chain when it leaves the pin?

In the given figure, the block of mass $m$ is dropped from the point $A$. The expression for the kinetic energy of the block when it reaches point $B$ is ................

Derive the work-energy theorem for a variable force exerted on a body in one dimension.

$A$ body of mass $10\, kg$ is released from a tower of height $20\, m$ and the body acquires a velocity of $10\, m/s$ after falling through the distance $20\, m$. The work done by the air resistance on the body is: ................. $J$ (Take $g = 10\, m/s^2$)

$A$ force acts on a $3 \,g$ particle in such a way that the position of the particle as a function of time is given by $x = 3t - 4t^2 + t^3$,where $x$ is in metres and $t$ is in seconds. The work done during the first $4 \,s$ is ..... $mJ$.

$A$ 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: