Energy of electron in the second orbit of hydrogen atom is $$\mathrm{E}$$. The energy of electron '$$\mathrm{E}_3$$' in the third orbit of helium $$(\mathrm{He})$$ atom will be

A series L-C-R circuit containing a resistance of $$120 ~\Omega$$ has angular frequency $$4 \times 10^5 \mathrm{~rad} \mathrm{~s}^{-1}$$. At resonance the voltage across resistance and inductor are $$60 \mathrm{~V}$$ and $$40 \mathrm{~V}$$ respectively, then the value of inductance will be

A body of mass 'M' and radius 'R', situated on the surface of the earth becomes weightless at its equator when the rotational kinetic energy of the earth reaches a critical value 'K'. The value of 'K' is given by [Assume the earth as a solid sphere, g = gravitational acceleration on the earth's surfacde]

A circuit has self-inductance 'L' H and carries a current 'I' A. To prevent sparking when the circuit is switched off, a capacitor which can withstand 'V' volt is used. The least capacitance of the capacitor connected across the switch must be equal to