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

The density of a metal at normal pressure $$p$$ is $$\rho$$. When it is subjected to an excess pressure, the density becomes $$\rho^{\prime}$$. If $$K$$ is the bulk modulus of the metal, then the ratio $$\frac{\rho^{\prime}}{\rho}$$ is

For a particle performing SHM when displacement is $$x$$, the potential energy and restoring force acting on it is denoted by $$E$$ and $$F$$, respectively. The relation between $$x, E$$ and $$F$$ is

Surface density of charge on a charged conducting sphere of radius $$R$$ in terms of electric field intensity $$E$$ at a distance $$r$$ in free space is ($$r>R, \varepsilon_0=$$ permittivity of free space)