In a cuboid of dimension \(2 L \times 2 L \times L\), a charge \(q\) is placed at the centre of the surface ' \(S\) ' having area of \(4 L ^2\). The flux through the opposite surface to ' \(S\) ' is given by

The electric field component of a monochromatic radiation is given by \(\vec E = 2{E_0}\,\hat i\,\cos\, kz\,\cos\, \omega t\) Its magnetic field \(\vec B\) is then given by

A sample of an ideal gas is taken through the cyclic process \(abca\) as shown in the figure. The change in the internal energy of the gas along the path \(ca\) is \(-180\, J\). The gas absorbs \(250\, J\) of heat along the path \(ab\) and \(60\, J\) along the path \(bc\). The work done by the gas along the path \(abc\) is ..... \(J\)

particle moves with simple harmonic motion in a straight line. In first \(\tau\ s\), after starting from rest it travels a distance \(a\), and in next \(\tau\ s\) it travels \(2a\), in same direction, then

A particle of mass \(250\,g\) executes a simple harmonic motion under a periodic force \(F =(-25\,x) N\). The particle attains a maximum speed of \(4\,m / s\) during its oscillation. The amplitude of the motion is \(...........cm\).

The pressure of a gas changes linearly with volume from \(A\) to \(B\) as shown in figure. If no heat is supplied to or extracted from the gas then change in the internal energy of the gas will be \(............\,J\)

A tub is filled with water and a wooden cube \(10\) cm \(\times\) \(10\) cm \(\times\) \(10\) cm is placed in the water. The wooden cube is found to float on the water with a part of it submerged in water. When a metal coin is placed on the wooden cube, the submerged part is increased by \(3.87\) cm. The mass of the metal coin is _______ gram.
(Take water density as \(1\) g/cm\(^3\) and density of wood as \(0.4\) g/cm\(^3\))

In Bohr's atomic model, the electron is assumed to revolve in a circular orbit of radius \(0.5 \times 10^{-10}\,m\). If the speed of electron is \(2.2 \times 10^{6} \;{m} / {s}\), then the current associated with the electron will be \(....\,\times 10^{-2} \;{mA}\). [Take \(\pi\) as \(\left.\frac{22}{7}\right]\)

An average force of \(125\,N\) is applied on a machine gun firing bullets each of mass \(10\,g\) at the speed of \(250\,m / s\) to keep it in position. The number of bullets fired per second by the machine gun is:

The energy associated with electric field is \((U_E)\) and with magnetic field is \((U_B)\) for an electromagnetic wave in free space. Then