Two rings of radius 'R' and 'nR' made of same material have the ratio of moment of inertia about an axis passing through its centre and perpendicular to the plane is $$1: 8$$. The value of '$$n$$' is (mass per unit length $$=\lambda$$)

Two rotating bodies $$P$$ and $$Q$$ of masses '$$\mathrm{m}$$' and '$$2 \mathrm{~m}$$' with moment of inertia $$I_P$$ and $$I_Q\left(I_Q > I_P\right)$$ have equal Kinetic energy of rotation. If $$\mathrm{L}_P$$ and $$\mathrm{L}_Q$$ be their angular momenta respectively then

A solid sphere of mass '$$M$$' and radius '$$R$$' is rotating about its diameter. A solid cylinder of same mass and same radius is also rotating about its geometrical axis with an angular speet twice that of the sphere. The ratio of the kinetic energy of rotation of the sphere to that of the cylinder is

A particle performs rotational motion with an angular momentum 'L'. If frequency of rotation is doubled and its kinetic energy becomes one fourth, the angular momentum becomes.