$A$ uniform rod of mass $M$ is hinged at its upper end. $A$ particle of mass $m$ moving horizontally strikes the rod at its mid point elastically. If the particle comes to rest after collision find the value of $M/m =?$

Two identical circular loops are moving with same kinetic energy one rolls $\&$ other slides. The ratio of their speed is 

A circular plate is rotating in horizontal plane, about an axis passing through its center and perpendicular to the plate, with an angular velocity $\omega$. A person sits at the center having two dumbbells in his hands. When he stretches out his hands, the moment of inertia of the system becomes triple. If $E$ be the initial Kinetic energy of the system, then final Kinetic energy will be $\frac{E}{x}$.The value of $x$ is $....$

$A$ uniform rod of mass $m$ and length $l$ hinged at its end is released from rest when it is in the horizontal position. The normal reaction at the hinge when the rod becomes vertical is :

The grinding stone of a flour mill is rotating at $600\, rad/sec$. for this power of  $1.2\, k\, watt$ is used. the effective torque on stone in $N-m$ will be

Two rotating bodies $A$ and $B$ of masses $m$ and $2\,m$ with moments of inertia $I_A$ and $I_B (I_B> I_A)$ have equal kinetic energy of rotation. If $L_A$ and $L_B$ be their angular momenta respectively, then