5.6 liter of helium gas at STP is adiabatically compressed to 0.7 liter. Taking the initial temperature to be T₁, the work done in the process is

Steel wire of lenght ‘L’ at 40^oC is suspended from the ceiling and then a mass ‘m’ is hung from its free end. The wire is cooled down from 40^oC to 30^oC to regain its original length ‘L’. The coefficient of linear thermal expansion of the steel is 10⁻⁵ /^oC, Young’s modulus of steel is 10¹¹ N/m² and radius of the wire is 1 mm. Assume that L >> diameter of the wire. Then the value of ‘m’ in kg is nearly

A police car with a siren of frequency 8 kHz is moving with uniform velocity 36 km/hr towards a tall building which reflects the sound waves. The speed of sound in air is 320 m/s. The frequency of the siren heard by the car driver is

A spherical metal shell A of radius $${R_A}$$ and a solid metal sphere $$B$$ of radius $${R_B}\left( { < {R_A}} \right)$$ are kept far apart and each is given charge $$' + Q'.$$ Now they are connected by a thin metal wire. Then