A body slides down a smooth inclined plane having angle $$\theta$$ and reaches the bottom with velocity $$v$$. If a body is a sphere, then its linear velocity at the bottom of the plane is

A thin uniform rod has mass $$M$$ and length $$L$$ The moment of inertia about an axis perpendicular to it and passing through the point at a distance $$\frac{L}{3}$$ from one of its ends, will be

The ratio of radii of gyration of a ring to a disc (both circular) of same radii and mass, about a tangential axis perpendicular to the plane is

If there is a change of angular momentum from $$1 \mathrm{j}$$-$$\mathrm{s}$$ to $$4 \mathrm{j}$$-$$\mathrm{s}$$ in $$4 \mathrm{~s}$$, then the torque