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
$\frac{1}{3}\,g\, \sin \, \theta$
$\frac{2}{3}\,g\, \sin \, \theta$
$\frac{2}{5}\,g\, \sin \, \theta$
$\frac{2}{7}\,g\, \sin \, \theta$
A wheel of mass $10\,kg$ has a moment of inertia of $160\,kg-m^2$ about its own axis. The radius of gyration is ........ $m.$
We have two spheres, one of which is hollow shell and the other solid. They have identical masses and moment of inertia about their respective diameters. The ratio of their radius is given by
Two particles which are initially at rest, move towards each other under the action of their internal attraction. If their speeds are $v$ and $2v$ at any instant, then the speed of centre of mass of the system will be
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
If the earth were to suddenly contract to $1/n^{th}$ of its present radius without any change in its mass, the duration (in $hrs.$ ) of the new day will be nearly