In a plane \(EM\) wave, the electric field oscillates sinusoidally at a frequency of \(5 \times 10^{10} \mathrm{~Hz}\) and an amplitude of \(50 \mathrm{Vm}^{-1}\). The total average energy density of the electromagnetic field of the wave is _______. [Use \(\varepsilon_0=8.85 \times 10^{-12} \mathrm{C}^2 / \mathrm{Nm}^2\) ]

A radioactive sample disintegrates via two independent decay processes having half lives \(T _{1 / 2}^{(1)}\) and \(T _{1 / 2}^{(2)}\) respectively. The effective half- life \(T _{1 / 2}\) of the nuclei is

Consider a gas of triatomic molecules. The molecules are assumed to the triangular and made of massless rigid rods whose vertices are occupied by atoms. The internal energy of a mole of the gas at temperature \(T\) is \(......RT\)

The intensity of the light from a bulb incident on a surface is \(0.22 \,W / m ^{2}\). The amplitude of the magnetic field in this light-wave is_______ \(\times 10^{-9} \,T\). (Given : Permittivity of vacuum \(\epsilon_{0}=8.85 \times 10^{-12} \,C ^{2} N ^{-1} m ^{-2}\), speed of light in vacuum \(c =3 \times 10^{8} \,ms ^{-1}\) )

A ball of mass \(0.5 \; kg\) is dropped from the height of \(10 \; m\). The height, at which the magnitude of velocity becomes equal to the magnitude of acceleration due to gravity, is \(\dots \; m\). (Use \(g =10 \; m / s ^{2}\)).

The angular momentum of an electron in a hydrogen atom is proportional to _______. (Where \(\mathrm{r}\) is the radius of orbit of electron)

The depth below the surface of sea to which a rubber ball be taken so as to decrease its volume by \(0.02 \%\) is ______ \(\mathrm{m}\). (Take density of sea water \(=10^3 \mathrm{kgm}^{-3}\), Bulk modulus of rubber \(=9 \times 10^8 \mathrm{Nm}^{-2}\), and \(\mathrm{g}=10 \mathrm{~ms}^{-2}\) )

A force acts on a \(2\,kg\) object so that its position is given as a function of time as \(x= 3t^2 + 5.\) What is the work done by this force in first \(5\,seconds\) ? ................ \(\mathrm{J}\)

A cone of base radius \(R\) and height \(h\) is located in a uniform electric field \(\vec E\) parallel to its base. The electric flux entering the cone is

A cylinder of radius \(R\) is surrounded by a cylindrical shell of inner radius \(R\) and outer radius \(2R\). The thermal conductivity of the material of the inner cylinder is \(K_1\) and that of the outer cylinder is \(K_2\). Assuming no loss of heat, the effective thermal conductivity of the system for heat flowing along the length of the cylinder is

If \(\lambda_{1}\) and \(\lambda_{2}\) are the wavelengths of the third member of Lyman and first member of the Paschen series respectively, then the value of \(\lambda_{1}: \lambda_{2}\) is

A rod with circular cross-section area \(2\,cm ^2\) and length \(40\,cm\) is wound uniformly with \(400\) turns of an insulated wire. If a current of \(0.4\,A\) flows in the wire windings, the total magnetic flux produced inside windings is \(4\,\pi \times 10^{-6}\,Wb\). The relative permeability of the rod is (Given : Permeability of  vacuum \(\left.\mu_0=4 \pi \times 10^{-7} \;NA ^{-2}\right)\)

In a Vernier Calipers. \(10\) divisions of Vernier scale is equal to the \(9\) divisions of main scale. When both jaws of Vernier calipers touch each other, the zero of the Vernier scale is shifted to the left of \(zero\) of the main scale and \(4^{\text {th }}\) Vernier scale division exactly coincides with the main scale reading. One main scale division is equal to \(1\,mm\). While measuring diameter of a spherical body, the body is held between two jaws. It is now observed that zero of the Vernier scale lies between \(30\) and \(31\) divisions of main scale reading and \(6^{\text {th }}\) Vernier scale division exactly. coincides with the main scale reading. The diameter of the spherical body will be \(.......cm\)