If \(\mu_0\) and \(\varepsilon_0\) are the permeability and permittivity of free space, respectively, then the dimension of \(\left(\frac{1}{\mu_0 \varepsilon_0}\right)\) is :

The electric field in an electromagnetic wave is given by \({E}=\left(50\, {NC}^{-1}\right) \sin \omega({t}-{x} / {c})\) The energy contained in a cylinder of volume \({V}\) is \(5.5 \times 10^{-12} \, {J}\). The value of \({V}\) is \(......{cm}^{3}\) \(\left(\right.\) given \(\left.\in_{0}=8.8 \times 10^{-12} \,{C}^{2} {N}^{-1} {m}^{-2}\right)\)

A \(0.5\) kg mass is in contact against the inner wall of a cylindrical drum of radius \(4\) m rotating about its vertical axis. The minimum rotational speed of the drum to enable the mass to remain stuck to the wall (without falling) is \(5\) rad/s. The coefficient of friction between the drum's inner wall surface and mass is _______. (Take \(g = 10\) m/s\(^2\))

A rod of linear mass density ' \(\lambda\) ' and length ' \(L\) ' is bent to form a ring of radius 'R'. Moment of inertia of ring about any of its diameter is :

Magnetic fields at two points on the axis of a circular coil at a distance of \(0.05\, m\) and \(0.2\, m\) from the centre are in the ratio \(8: 1.\) The radius of coil is .......... \(m\)

Magnetic materials used for making permanent magnets \((P)\) and magnets in a transformer \((T)\) have different properties of the following, which property best matches for the type of magnet required \(?\)

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

An object \(AB\) is placed \(15\text{ cm}\) on the left of a convex lens \(P\) of focal length \(10\text{ cm}\). Another convex lens \(Q\) is now placed \(15\text{ cm}\) right of lens \(P\). If the focal length of lens \(Q\) is \(15\text{ cm}\), the final image is _______.

Consider a finite insulated, uncharged conductor placed near a finite positively charged conductor. The uncharged body must have a potential

A nucleus with mass number \(242\) and binding energy per nucleon as \(7.6\,MeV\) breaks into fragment each with mass number \(121\) . If each fragment nucleus has binding energy per nucleon as \(8.1\,MeV\), the total gain in binding energy is \(........MeV\)

A radioactive nucleus \(n_2\) has 3 times the decay constant as compared to the decay constant of another radioactive nucleus \(n_1\). If initial number of both nuclei are the same, what is the ratio of number of nuclei of \(n_2\) to the number of nuclei of \(n_1\), after one half-life of \(n_1\) ?

Two conductors have the same resistances at \(0^{\circ} \mathrm{C}\) but their temperature coefficients of resistance are \(\alpha_1\) and \(\alpha_2\). The respective temperature coefficients for their series and parallel combinations are _______.

For a transparent prism, if the angle of minimum deviation is equal to its refracting angle, the refractive index n of the prism satisfies.