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

Consider an electric field $$\overrightarrow E = {E_0}\widehat x$$ where $${E_0}$$ is a constant. The flux through the shaded area (as shown in the figure) due to this field is

A $$2$$ $$\mu F$$ capacitor is charged as shown in the figure. The percentage of its stored energy dissipated after the switch $$S$$ is turned to position $$2$$ is