Four identical uniform solid spheres each of same mass $$M$$ and radius $$R$$ are placed touching each other as shown in figure with centres $$A, B, C, D. I_A, I_B, I_C, I_D$$ are the moment of inertia of these spheres respectively about an axis passing through centre and perpendicular to the plane, then

A thin uniform $$\operatorname{rod} A B$$ of mass $$m$$ and length $$l$$ is hinged at one end $$A$$ to the ground level. Initially the rod stands vertically and is allowed to fall freely to the ground in the vertical plane. The angular velocity of the rod when its end $$B$$ strikes the ground is ( $$g=$$ acceleration due to gravity)

A rigid body rotates with an angular momentum L. If its rotational kinetic energy is made four times, its angular momentum will become

The rotational kinetic energy and translational kinetic energy of a rolling body are same, the body is