The critical angle of a medium for a specific wavelength, if the medium has relative permittivity \(3\) and relative permeability \(\frac{4}{3}\) for this wavelength, will be.....\(^o\)

Consider a sphere of radius \(\mathrm{R}\) which carries a uniform charge density \(\rho .\) If a sphere of radius \(\frac{\mathrm{R}}{2}\) is carved out of it, as shown, the ratio \(\frac{\left|\overrightarrow{\mathrm{E}}_{\mathrm{A}}\right|}{\left|\overrightarrow{\mathrm{E}}_{\mathrm{B}}\right|}\) of magnitude of electric field \(\overrightarrow{\mathrm{E}}_{\mathrm{A}}\) and \(\overrightarrow{\mathrm{E}}_{\mathrm{B}}\) respectively, at points \(\mathrm{A}\) and \(\mathrm{B}\) due to the remaining portion is

The fifth harmonic of a closed organ pipe is found to be in unison with the first harmonic of an open pipe. The ratio of lengths of closed pipe to that of the open pipe is \(5 / x\). The value of \(x\) is _________ .

A circular coil having \(200\) turns, \(2.5 \times 10^{-4} \mathrm{~m}^2\) area and carrying \(100 \mu \mathrm{A}\) current is placed in a uniform magnetic field of \(1 \mathrm{~T}\). Initially the magnetic dipole moment \((\vec{M})\) was directed along \(\vec{B}\). Amount of work, required to rotate the coil through \(90^{\circ}\) from its initial orientation such that \(\overrightarrow{\mathrm{M}}\) becomes perpendicular to \(\vec{B}\) is _______ \(\mu \mathrm{J}\).

A light planet is revolving around a massive star in a circular orbit of radius \(R\) with a period of revolution \(T\). If the force of attraction between planet and star is proportional to \(\mathrm{R}^{-3 / 2}\) then choose the correct option.

A wire of resistance \(9 \Omega\) is bent to form an equilateral triangle. Then the equivalent resistance across any two vertices will be _____ ohm.

The velocity of a particle is given as \(\vec{v} = -x\hat{i} + 2y\hat{j} - z\hat{k}\) m/s. The magnitude of acceleration at point \((1, 2, 4)\) is _______ m/s\(^2\).

In an experiment to determine the period of a simple pendulum of length \(1\, m\), it is attached to different spherical bobs of radii \(r_1\) and \(r_2\) . The two spherical bobs have uniform mass distribution. If the relative difference in the periods, is found to be \(5\times10^{-4}\, s\), the difference in radii, \(\left| {{r_1} - {r_2}} \right|\) is best given by .... \(cm\)

If the distance between object and its two times magnified virtual image produced by a curved mirror is \(15 \mathrm{~cm}\), the focal length of the mirror must be _______.

The figure represents the momentum time \((p-t)\) curve for a particle moving along an axis under the influence of the force. Identify the regions on the graph where the magnitude of the force is maximum and minimum respectively ? If \(\left(t_3-t_2\right) < t_1\)

Which level of the single ionized carbon has the same energy as the ground state energy of hydrogen atom ?

The aperture of the objective is \(24.4\,cm\). The resolving power of this telescope. If a light of wavelength \(2440 \mathring A\) is used to see the object will be