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

A solid cylinder of mass $$3 \mathrm{~kg}$$ is rolling on a horizontal surface with velocity $$4 \mathrm{~m} / \mathrm{s}$$. It collides with a horizontal spring whose one end is fixed to rigid support. The force constant of material of spring is $$200 \mathrm{~N} / \mathrm{m}$$. The maximum compression produced in the spring will be (assume collision between cylinder & spring be elastic)