A light ray is incident on a glass slab of thickness \(4 \sqrt{3} \mathrm{~cm}\) and refractive index \(\sqrt{2}\). The angle of incidence is equal to the critical angle for the glass slab with air. The lateral displacement of ray after passing through glass slab is _______ \(\mathrm{cm}\). \(\left(\right.\) Given \(\left.\sin 15^{\circ}=0.25\right)\)

Assume that the earth is a solid sphere of uniform density and a tunnel is dug along its diameter throughout the earth. It is found that when a particle is released in this tunnel, it executes a simple harmonic motion. The mass of the particle is \(100 g\). The time period of the motion of the particle will be (approximately) (take \(g =10\,ms ^{-2}\), radius of earth \(=6400\,km\) )

An electron rotates in a circle around a nucleus having positive charge \(\mathrm{Ze}\). Correct relation between total energy ( \(E\) ) of electron to its potential energy \((U)\) is _______.

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 coil is placed in a time varying magnetic field. If the number of turns in the coil were to be halved and the radius of wire doubled, the electrical power dissipated due to the current induced in the coil would be: (Assume the coil to be short circuited.)

A sonometer wire oflength \(1.5\ m\) is made of steel. The tension in it produces an elastic strain of \(1 \%\). What is the fundamental frequency of steel if density and elasticity of steel are \(7.7 \times 10^3 \) \(kg/m^3\) and \(2.2 \times 10^{11}\) \(N/m^2\) respectively?

The distance between Sun and Earth is \(R.\) The duration of year if the distance between Sun and Earth becomes \(3R\) will be 

An inductor of reactance \(100 \Omega\), a capacitor of reactance \(50 \Omega\), and a resistor of resistance \(50 \Omega\) are connected in series with an AC source of 10 V , 50 Hz. Average power dissipated by the circuit is ________ W.

The electric field in a region of space is given by, \(\overrightarrow E  = {E_0}\hat i + 2{E_0}\hat j\) where \(E_0\, = 100\, N/C\). The flux of the field through a circular surface of radius \(0.02\, m\) parallel to the \(Y-Z\) plane is nearly

Two identical solid spheres each of mass \(2\,kg\) and radii \(10\,cm\) are fixed at the ends of a light rod. The separation between the centres of the spheres is \(40\,cm\). The moment of inertia of the system about an axis perpendicular to the rod passing through its middle point is \(........... \times 10^{-3}\,kg - m ^2\)

A diatomic gas \((\gamma=1.4)\) does \(400 J\) of work when it is expanded isobarically. The heat given to the gas in the process is ............ \(J\)

A beam of electromagnetic radiation of intensity \(6.4 \times 10^{-5}\; \mathrm{W} / \mathrm{cm}^{2}\) is comprised of wavelength, \(\lambda=310 \;\mathrm{nm} .\) It falls normally on a metal (work function \(\varphi=2 \;\mathrm{eV}\) ) of surface area of \(1\; \mathrm{cm}^{2} .\) If one in \(10^{3}\) photons ejects an electron, total number of electrons ejected in \(1 \;s\) is \(10^{\mathrm{x}}\).then \(\mathrm{x}\) is \(\left(\mathrm{hc}=1240\; \mathrm{eV} \mathrm{nm}, 1\; \mathrm{eV}=1.6 \times 10^{-19} \;\mathrm{J}\right)\)