Two small drops of mercury each of radius $$r$$ coalesce to form a large single drop. The ratio of the total surface energies before and after the change is

A solid cylinder of radius $$r$$ and mass $$M$$ rolls down an inclined plane of height $$h$$. When it reaches the bottom of the plane, then its rotational kinetic energy is ($$g=$$ acceleration due to gravity)

A potentiometer wire is $$4 \mathrm{~m}$$ long and potential difference of $$3 \mathrm{~V}$$ is maintained between the ends. The emf of the cell, which balances against a length of $$100 \mathrm{~cm}$$ of the potentiometer wire is

A charged particle is moving in a uniform magnetic field in a circular path of radius $$R$$. When the energy of the particle becomes three times the original, the new radius will be