A mass '$$M$$' is moving with constant velocity parallel to $$\mathrm{X}$$-axis. Its angular momentum with respect to the origin is

A thin uniform rod of mass '$$m$$' and length '$$P$$' is suspended from one end which can oscillate in a vertical plane about the point of intersection. It is pulled to one side and then released. It passes through the equilibrium position with angular speed '$$\omega$$'. The kinetic energy while passing through mean position is

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)