\(5\, beats/ second\) are heard when a turning fork is sounded with a sonometer wire under tension, when the length of the sonometer wire is either \(0.95\,m\) or \(1\,m\) . The frequency of the fork will be ... \(Hz\)

What will be the average value of energy along one degree of freedom for an ideal gas in thermal equilibrium at a temperature \(T \,?\left( k _{ B }\right.\) is Boltzmann constant)

A parallel plate capacitor of capacitance \(12.5 \mathrm{pF}\) is charged by a battery connected between its plates to potential difference of \(12.0 \mathrm{~V}\). The battery is now disconnected and a dielectric slab \(\left(\epsilon_{\mathrm{r}}=6\right)\) is inserted between the plates. The change in its potential energy after inserting the dielectric slab is _______.\(\times 10^{-12} \mathrm{~J}\).

Given below are two statement: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A:\) If an electric dipole of dipole moment \(30 \times 10^{-5}\,Cm\) is enclosed by a closed surface, the net flux coming out of the surface will be zero. Reason \(R\) : Electric dipole consists of two equal and opposite charges. In the light of above, statements, choose the correct answer from the options given below:

Arrange the four graphs in descending order of total work done; where \(W _{1}, W _{2}, W _{3}\) and \(W _{4}\) are the work done corresponding to figure \(a , b , c\) and d respectively.

An electric bulb rated as \(200\, {W}\) at \(100 \,{V}\) is used in a circuit having \(200\, {V}\) supply. The resistance \('R'\) that must be put in series with the bulb so that the bulb delivers the same power is \(.....\,\Omega\)

A circular disc of radius \(b\) has a hole of radius \(a\) at its centre (see figure). If the mass per unit area of the disc varies as \(\left( {\frac{{{\sigma _0}}}{r}} \right)\), then the radius of gyration of the disc about its axis passing through the centre is

A Carnot engine take \(5000 \,k\,cal\) of heat from a reservoir at \(727\,^{\circ}C\) and gives heat to a \(\operatorname{sink}\) at \(127\,^{\circ}C\). The work done by the engine is \(.......... \times 10^{6}\,J\)

The de Broglie wavelength of a molecule in a gas at room temperature \((300\,K )\) is \(\lambda_1\). If the temperature of the gas is increased to \(600\,K\), then the de Broglie wavelength of the same gas molecule becomes \(..............\).

The distance between two consecutive points with phase difference of \(60^{\circ}\) in a wave of frequency \(500\,Hz\) is \(6.0\,m\). The velocity with which wave is traveling is \(.........km / s\)

The mean intensity of radiation on the surface of the Sun is about \(10^{8}\,W/m^2.\) The \(rms\) value of the corresponding magnetic field is closet to