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 

For a rolling body, the velocity of $P_1$ and $P_2$ are ${\vec v_1}$ and ${\vec v_2}$ , respectively

A circular disc is rolling on a horizontal plane. Its total kinetic energy is $300\, J$. ........ $J$ is its translational $K.E.$

A disc initially at rest, is rotated about its axis with a uniform angular acceleration. In the first $2$ $s$ , it rotates an angle $\theta$. In the next $2\, s$, the disc will rotate through an angle

A spherical uniform body of radius $R$, mass $M$ and moment of inertia $I$ rolls down (without slipping) on an inclined plane making an angle $\theta $ with the horizontal. Then its acceleration is

The linear mass density of a rod of length $L$ varies as $\lambda = kx^2$, where $k$ is a  constant and $x$ is the distance from one end. The position of centre of mass of the  rod is