$A$ hemisphere of radius $R$ and mass $4m$ is free to slide with its base on a smooth horizontal table. $A$ particle of mass $m$ is placed on the top of the hemisphere. The angular velocity of the particle relative to the hemisphere at an angular displacement $\theta$ when the velocity of the hemisphere is $v$ is:

What is a rigid body? Explain the difference between a rigid body and a solid body.

What is pure translational motion?

In pure translational motion,the velocity of every particle of a body at any instant is what? Equal or unequal?

What is the direction of angular velocity for a rigid body?

The pulley shown in the figure is made using a thin rim and two rods of length equal to the diameter of the rim. The rim and each rod have a mass of $M$. Two blocks of mass $M$ and $m$ are attached to two ends of a light string passing over the pulley,which is hinged to rotate freely in a vertical plane about its centre. The magnitude of the acceleration experienced by the blocks is . . . . . . (assume no slipping of the string on the pulley.)