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)

A body is thrown from the surface of the earth velocity $$\mathrm{v} / \mathrm{s}$$. The maximum height above the earth's surface upto which it will reach is ($$R=$$ radius of earth, $$g=$$ acceleration due to gravity)

Using Bohr's quantisation condition, what is the rotational energy in the second orbit for a diatomic molecule? ($$I=$$ moment of inertia of diatomic molecule and, $$h=$$ Planck's constant)