If the ratio of specific heat of a gas at constant pressure to that at constant volume is $$\gamma$$, the change in internal energy of the given mass of gas, when the volume changes from $$V$$ to $$2 V$$ at constant pressure $$p$$ is

A coil of 100 turns and area $$2 \times 10^{-2} \mathrm{~m}^2$$ is pivoted about a vertical diameter in a uniform magnetic field and carries a current of $$5 \mathrm{~A}$$. When the coil is held with its plane in North-South direction, it experiences a couple of $$0.33 \mathrm{~N}-\mathrm{m}$$. When the plane is East-West, the corresponding couple is $$0.4 \mathrm{~N}-\mathrm{m}$$. The value of magnetic induction is [Neglect earth's magnetic field]

A man stands between two parallel cliffs (not in middle). When he claps his hands, he hears two echoes one after is and the other after $$2 \mathrm{~s}$$. If the velocity of sound in air is $$330 \mathrm{~m} / \mathrm{s}$$, the width of the cliff is

Light of wavelength $$\lambda$$ strikes a photoelectric surface and electrons are ejected with kinetic energy $$K$$. If $$K$$ is to be increased to exactly twice its original value, the wavelength must be changed to $$\lambda^{\prime}$$, such that