Two circular loop $A$ and $B$ of radii $R$ and $N R$ respectively are made from a uniform wire. Moment of inertia of $B$ about its axis is 3 times that of $A$ about its axis. The value of $N$ is

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