In a rectangle $ABCD (BC = 2AB)$. The moment of inertia will be minimum along the axis :-

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 ............

A uniform solid sphere of mass $m$ and radius $r$ rolls without slipping down a inclined plane, inclined at an angle $45^o$ to the horizontal. Find the magnitude of frictional coefficient at which slipping is absent

A circular disk of moment of inertia $I_t$ is rotating in a horizontal plane, about its symmetry axis, with a constant angular speed ${\omega _i}$. Another disk of moment of inertia $I_b$ is dropped coaxially onto the rotating disk. Initially the second disk has zero angular speed. Eventually both the disks rotate with a constant angular speed ${\omega _f}$. The energy lost by the initially rotating disc to friction is

If a solid sphere is rolling the ratio of its rotational energy to the total kinetic energy is given by

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 ..