Find the torque about the origin when a force of  acts on a particle whose position vector is .

Two particles of mass  and  respectively are attached to the two ends of a rigid rod of length  with negligible mass. The centre of mass of the system from the  particle is nearly at a distance of :

From a circular ring of mass '  ' and radius '  ' an arc corresponding to a  sector is removed. The moment of inertia of the remaining part of the ring about an axis passing through the centre of the ring and perpendicular to the plane of the ring is '  ' times '  '. Then the value of '  ' is 

A uniform rod of length  and mass  is balanced on a wedge placed at  mark. A mass of  is suspended from the rod at  and another unknown mass '  ' is suspended from the rod at  mark as shown in the figure. Find the value of '  ' such that the rod is in equilibrium.                                                                  

Two objects of mass  and  respectively are connected to the two ends of a rigid rod of length  with negligible mass. The distance of the center of mass of the system from the  mass is:

The ratio of the radius of gyration of a thin uniform disc about an axis passing through its centre and normal to its plane to the radius of gyration of the disc about its diameter is:

The angular acceleration of a body, moving along the circumference of a circle, is

The ratio of radius of gyration of a solid sphere of mass  and radius  about its own axis to the radius of gyration of the thin hollow sphere of same mass and radius about its axis is