Electromagnetic waves travel in a medium with speed of \(1.5 \times 10^8 \mathrm{~ms}^{-1}\). The relative permeability of the medium is \(2.0\) . The relative permittivity will be _______.

A small bulb is placed at the bottom of a tank containing water to a depth of \(\sqrt{7} \; m\). The refractive index of water is \(\frac{4}{3}\). The area of the surface of water through which light from the bulb can emerge out is \(x \,\pi m ^{2}\). The value of \(x\) is ...............

The equation of a plane progressive wave is given by \(y = 5\cos\pi\left(200t - \dfrac{x}{150}\right)\) where \(x\) and \(y\) are in cm and \(t\) is in second. The velocity of the wave is _______ m/s.

A body of mass \(2\,kg\) is initially at rest. It starts moving unidirectionally under the influence of a source of constant 10.Power P. Its displacement in \(4\,s\) is \(\frac{1}{3} \alpha^2 \sqrt{ P } m\). The value of \(\alpha\) will be \(.............\)

Two satellites, \(A\) and \(B,\) have masses \(m\) and \(2\,m\) respectively. \(A\) is in a circular orbit of radius \(R,\) and \(B\) is in a circular orbit of radius \(2R\) around the earth. The ratio of their kinetic energies, \(K.E._A / K.E._B ,\) is

Nitrogen gas is at \(300^{\circ} C\) temperature. The temperature (in \(K\)) at which the \(rms\) speed of a \(H _{2}\), molecule would be equal to the \(rms\) speed of a nitrogen molecule, is........ (Molar mass of \(N _{2}\) gas \(28\, g\) )

In the given circuit, an ideal voltmeter connected across the \(10\,\Omega \) resistance reads \(2\, V\). The internal resistance \(r\), of each cell is ................... \(\Omega\)

In free space, an electromagnetic wave of \(3 \; GHz\) of \(3 \; GHz\) frequency strikes over the edge of an object of size \(\frac{\lambda}{100}\), where \(\lambda\) is the wavelength of the wave in free space. The phenomenon, which happens there will be .....

The terminal velocity of a metallic ball of radius 6 mm in a viscous fluid is \(20 cm / s\). The terminal velocity of another ball of same material and having radius 3 mm in the same fluid will be _________ \(cm / s\).

A body of mass \(5\, kg\) under the action of constant force \(\overrightarrow F  = {F_x}\hat i + {F_y}\hat j\) has velocity at \(t\,= 0\, s\) as \(\overrightarrow v  = \left( {6\hat i - 2\hat j\,m/s} \right)\)  and at \(t\, = 10\,s\) as \(\overrightarrow v  = +6\hat j\,m/s\). The force \(\overrightarrow F \) is 

The energy released in the fusion of \(2 \mathrm{~kg}\) of hydrogen deep in the sun is \(\mathrm{E}_{\mathrm{H}}\) and the energy released in the fission of \(2 \mathrm{~kg}\) of \({ }^{235} \mathrm{U}\) is \(E_U\). The ratio \(\frac{E_H}{E_U}\) is approximately _______. (Consider the fusion reaction as \(4{ }_1^1 \mathrm{H}+2 \mathrm{e}^{-} \rightarrow{ }_2^4 \mathrm{He}+2 \mathrm{v}+6 \gamma+26.7 \mathrm{MeV}\), energy released in the fission reaction of \({ }^{235} \mathrm{U}\) is \(200 \mathrm{MeV}\) per fission nucleus and \(\mathrm{N}_{\mathrm{A}}=6.023 \times 10^{23}\) )

The current \((i)\) at time \(t =0\) and \(t =\infty\) respectively for the given circuit is

Wax is coated on the inner wall of a capillary tube and the tube is then dipped in water. Then, compared to the unwaxed capillary, the angle of contact \(\theta \) and the height \(h\) upto which water rises change. These changes are