A solid cylinder is released from rest from the top of an inclined plane of inclination $30^{\circ}$ and length 60 cm . If the cylinder rolls without slipping, then the speed when it reaches the bottom is

A solid sphere of mass 2 kg rolls on a smooth horizontal surface at $10 \mathrm{~m} / \mathrm{s}$. It then rolls up a smooth inclined plane of inclination $30^{\circ}$ with the horizontal. The height attained by the sphere before it stops is [take $g=10 \mathrm{~m} / \mathrm{s}^2$ ]

A rod of length $L$ revolves in a horizontal plane about the axis passing through its centre and perpendicular to its length. The angular velocity of the rod is $\omega$. If $A$ is the area of cross-section of the rod and $\rho$ is its density, then the rotational kinetic energy of the rod is

A solid sphere and a solid cylinder, each of mass $M$ and radius $R$ are rolling with a linear speed on a flat surface without slipping. Let $L_1$ be magnitude of the angular momentum of the sphere with respect to a fixed point along the path of the sphere. Likewise $L_2$ be the magnitude of angular momentum of the cylinder with respect to the same fixed point along its path. The ratio $L_1 / L_2$ is