5.40 A thin circular loop of radius R rotates about its vertical diameter with an angular frequency $\mathit{\omega }$ . Show that a small bead on the wire loop remains at its lowermost point for $\le \sqrt{\mathit{g}/\mathit{R}}$ . What is the angle made by the radius vector joining the centre to the bead with the vertical downward direction for $\mathit{}\mathit{\omega }$ = $\sqrt{2\mathit{g}/\mathit{R}}$ ? Neglect friction.

Two blocks of mass 10 kg and 5 kg are connected with a light string which passing over an ideal pulley attached with a fixed smooth wedge. If the system is released from rest, then the acceleration of the blocks will be

A block rests on an inclined plane making an angle of 30° with the horizontal. The coefficient of static friction between block and the plane is 0.8. If the frictional force on the block is 10 N, then mass of block (in kg) (Take g = 10 m/s² )

Bullets of 0.03 kg mass each hit a plate at a rate of 200 bullets per second with velocity of 50 m/s and reflect back with velocity of 30 m/s. The average force acting on the plate in newton is

The root mean square speed of molecules of a gas is 1260 m/s. The average speed of the gas molecules is

Find the acceleration of 2 kg block shown in the diagram. (neglect friction)