A spherical surface of radius of curvature '$$R$$' separates air from glass of refractive index 1.5. The centre of curvature is in the glass. A point object $$\mathrm{P}$$ placed in air forms a real image $$\mathrm{Q}$$ in the glass. The line $$P Q$$ cuts the surface at point '$$O$$' and $$\mathrm{PO}=\mathrm{OQ}=\mathrm{x}$$. Hence the distance '$$\mathrm{x}$$' is equal to

The rotational kinetic energy and translational kinetic energy of a rolling body are same, the body is

Two concentric circular coils A and B have radii $$20 \mathrm{~cm}$$ and $$10 \mathrm{~cm}$$ respectively lie in the same plane. The current in coil A is $$0.5 \mathrm{~A}$$ in anticlockwise direction. The current in coil B so that net field at the common centre is zero, is

A charged spherical conductor of radius '$$R$$' is connected momentarily to another uncharged spherical conductor of radius '$$r$$' by means of a thin conducting wire, then the ratio of the surface charge density of the first to the second conductor is