A disc of mass $m$ and radius $r$ is free to rotate about its centre as shown in the figure. A string is wrapped over its rim and a block of mass $m$ is attached to the free end of the string. The system is released from rest. The speed of the block as it descends through a height $h$, is .....
$\sqrt{2 g h}$
$\sqrt{\frac{2}{3} g h}$
$2 \sqrt{\frac{g h}{3}}$
$\frac{1}{2} \sqrt{3 g h}$
A solid cylinder of mass $M$ and radius $R$ rolls down an inclined plane without slipping. The speed of its centre of mass when it reaches the bottom is ...
When a body is rolling without slipping on a rough horizontal surface, the work done by friction is ........
Four point masses are fastened to the corners of $a$ frame of negligible mass lying in the $xy$ plane. Let $w$ be the angular speed of rotation. Then
Three particles are situated on a light and rigid rod along $Y$axis as shown in the figure. If the system is rotating with an angular velocity of $2\,rad/\sec $about $X$axis, then the total kinetic energy of the system is ...... $J$
A rod of length $50\,cm$ is pivoted at one end. It is raised such that if makes an angle of $30^o$ fro the horizontal as shown and released from rest. Its angular speed when it passes through the horizontal (in $rad\,s^{-1}$ ) will be $(g = 10\,ms^{-2})$