Find the torque about the origin when a force of 3 $$\hat j$$ N acts on a particle whose position vector is 2 $$\hat k$$ m.

A solid cylinder of mass 2 kg and radius 4 cm is rotating about its axis at the rate of 3 rpm. The torque required to stop after 2$$\pi $$ revolutions is :

Two particles A and B are moving in uniform circular motion in concentric circles of radii r_A and r_B with speed v_A and v_B respecitively. Their time period of rotation is the same. The ratio of angular speed of A to that of B will be :

A disc of radius 2 m and mass 100 kg rolls on a horizontal floor. Its centre of mass has speed of 20 cm/s. How much work is needed to stop it?