A solid cylinder of mass $M$ and radius $R$ rolls without slipping down an inclined plane of length $L$ and height $h$. What is the speed of its centre of mass when the cylinder reaches its bottom
$\sqrt {2\,gh}$
$\sqrt {\frac {3}{4}\,gh}$
$\sqrt {\frac {4}{3}\,gh}$
$\sqrt {4\,gh}$
A solid cylinder of mass $M$ and radius $R$ rolls without slipping down an inclined plane making an angle $\theta $ with the horizontal. then its acceleration is
The magnitude of displacement of a particle moving in a circle of radius $a$ with constant angular speed $\omega$ varies with time $t$ as
Particles of masses $m, 2m, 3m, ...... nm$ $grams$ are placed on the same line at distances $l, 2l, 3l,...., nl\, cm$ from a fixed point. The distance of the centre of mass of the particles from the fixed point (in centimetres) is
A rod $PQ$ of mass $M$ and length $L$ is hinged at end $P$. The rod is kept horizontal by a massless string tied to point $Q$ as shown in figure. When string is cut, the initial angular acceleration of the rod is
A cylinder of mass $M$ and radius $r$ is mounted on a frictionless axle over a well. A rope of negligible mass is wrapped around the solid cylinder and a bucket of mass $m$ is suspended from the rope. The linear acceleration of the bucket will be