Two particles of equal masses have velocities$\overrightarrow {{v_1}}  = 2\hat i\,m/s$ and $\overrightarrow {{v_2}}  = 2\hat j\,m/s$. The first particle has an acceleration $\overrightarrow {{a_1}}  = \left( {3i + 3\hat j} \right)\,m/{s^2}$,while the acceleration of the other particle is zero. The centre of mass of the two particles moves in a

A thin circular ring of mass $M$ and radius $R$ is rotating about its axis with a constant angular velocity $\omega $. Two objects, each of mass $m$, are attached gently to the opposite ends of a diameter of the ring. The ring rotates now with an angular velocity

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

Solid spherical ball is rolling on a frictionless horizontal plane surface about its axis of symmetry. The ratio of rotational kinetic energy of the ball to its total kinetic energy is ................

If the equation for the displacement of a particle moving on a circular path is given by:

                               $\theta  = 2t^3 + 0.5$

Where $\theta $ is in radian and $t$ in second, then the angular velocity of the particle at $t = 2\,sec$ is $t=$ ....... $rad/sec$

Let $F $ be the force acting on a particle having position vector $\vec r$ and $\vec T$ be the torque of this force about the origin.  Then ..