Two particles having mass $'M'$ and $'m'$ are moving in circular paths having radii $R$ and $ r.$ If their time periods are same then the ratio of their angular velocities will
$\frac{r}{R}$
$\frac{R}{r}$
$1$
$\sqrt {\frac{R}{r}} $
If the earth were to suddenly contract to $\frac {1}{n}^{th}$ of its present radius without any change in its mass the duration of the new day will be nearly
A disc of mass $M$ and radius $R$ is rolling with angular speed $\omega $ on a horizontal plane as shown. The magnitude of angular momentum of the disc about the origion $O$ is
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
The centre of mass of a body
An object slides down a smooth incline and reaches the bottom with velocity $v$. If same mass is in the form of a ring and it rolls down an inclined plane of same height and angle of inclination, then its velocity at the bottom of inclined plane will be ............