A vessel of depth 2h is half filled with a liquid of refractive index $$2\sqrt 2 $$ and the upper half with another liquid of refractive index $$\sqrt 2 $$ . The liquids are immiscible. The apparent depth of the inner surface of the bottom of vessel will be :

Consider two ideal diatomic gases A and B at some temperature T. Molecules of the gas A are rigid, and have a mass m. Molecules of the gas B have an additional vibrational mode, and have a mass $${m \over 4}$$ . The ratio of the specific heats ($$C_V^A$$ and $$C_V^B$$ ) of gas A and B, respectively is :

The electric fields of two plane electromagnetic plane waves in vacuum are given by
$$\overrightarrow {{E_1}} = {E_0}\widehat j\cos \left( {\omega t - kx} \right)$$ and
$$\overrightarrow {{E_2}} = {E_0}\widehat k\cos \left( {\omega t - ky} \right)$$
At t = 0, a particle of charge q is at origin with
a velocity $$\overrightarrow v = 0.8c\widehat j$$ (c is the speed of light in vacuum). The instantaneous force experienced by the particle is :

Radiation, with wavelength 6561 $$\mathop A\limits^o $$ falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of 3 × 10^–4 T. If the radius of the largest circular path followed by the electrons is 10 mm, the work function of the metal is close to :