$A$ string is wrapped around a disc of mass $M$ and radius $R$ and the free end is fixed to the ceiling. The centre of mass falls down as the disc unwinds the string. The tension in the string is

Two masses $m$ and $2m$ are connected by a light string passing over a pulley (disc) of mass $M = 30m$ and radius $r = 0.1 \ m$. The pulley is mounted in a vertical plane and is free to rotate about its axis. The $2m$ mass is released from rest. Find its speed when it has descended through a height of $h = 3.6 \ m$. (Assume the string does not slip and $g = 10 \ m/s^2$)

What is a rigid body?

$A$ flywheel is accelerated uniformly from rest and rotates through $5 \, rad$ in the first second. The angle rotated by the flywheel in the next second will be ......... $rad$.

$A$ rod of length $1 \ m$ is held vertically. What will be the speed of the other end when it touches the ground without slipping?

$A$ ladder of length $L$ is slipping with its ends against a vertical wall and a horizontal floor. At a certain moment,the speed of the end in contact with the horizontal floor is $v$ and the ladder makes an angle $\alpha = 30^o$ with the horizontal. If $dv/dt = 0$,then the angular acceleration of the ladder when $\alpha = 45^o$ is: