A diatomic gas with rigid molecules does \(10\, J\) of work when expanded at constant pressure. What would be the heat energy absorbed by the gas, in this process ..... \(J\).

A \(2 \mathrm{~kg}\) brick begins to slide over a surface which is inclined at an angle of \(45^{\circ}\) with respect to horizontal axis. The co-efficient of static friction between their surfaces is _______.

Match List \(I\) with List \(II\)

List - \(I\)	List - \(II\)
\((A)\) Torque	\((I)\) \({\left[\mathrm{M}^1 \mathrm{~L}^1 \mathrm{~T}^{-2} \mathrm{~A}^{-2}\right]}\)
\((B)\) Magnetic fileld	\((II)\) \(\left[\mathrm{L}^2 \mathrm{~A}^1\right]\)
\((C)\) Magneti moment	\((III)\) \({\left[\mathrm{M}^1 \mathrm{~T}^{-2} \mathrm{~A}^{-1}\right]}\)
\((D)\) permeability of free space	\((IV)\) \(\left[\mathrm{M}^1 \mathrm{~L}^2 \mathrm{~T}^{-2}\right]\)

Choose the correct answer from the options given below :

An object is allowed to fall from a height \(R\) above the earth, where \(R\) is the radius of earth. Its velocity when it strikes the earth's surface, ignoring air resistance, will be :

Find the ratio of energies of photons produced due to transition of an election of hydrogen atom from its \((i)\) second permitted energy level to the first level, and \((ii)\) the highest permitted energy level to the first permitted level.

A small bob of mass 100 mg and charge \(+10 \mu \mathrm{C}\) is connected to an insulating string of length 1 m. It is brought near to an infinitely long nonconducting sheet of charge density ' \(\sigma\) ' as shown in figure. If string subtends an angle of \(45^{\circ}\) with the sheet at equilibrium the charge density of sheet will be :
(Given, \(\varepsilon_0=8.85 \times 10^{-12} \frac{\mathrm{~F}}{\mathrm{~m}}\) and acceleration due to gravity, \(g=10 \mathrm{~m} / \mathrm{s}^2\))

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 .... \(cm\)

An electron with energy \(0.1\,ke\,V\) moves at right angle to the earth's magnetic field of \(1 \times 10^{-4}\,Wbm ^{-2}\). The frequency of revolution of the electron will be. (Take mass of electron \(=9.0 \times 10^{-31}\,kg\) )

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : In an insulated container, a gas is adiabatically shrunk to half of its initial volume. The temperature of the gas decreases.
Reason (R): Free expansion of an ideal gas is an irreversible and an adiabatic process.
In the light of the above statements, choose the correct answer from the options given below :

A bar magnet having a magnetic moment of \(2.0 \times\) \(10^{5} \; JT ^{-1}\), is placed along the direction of uniform magnetic field of magnitude \(B =14 \times 10^{-5}\; T\). The work done in rotating the magnet slowly through \(60^{\circ}\) from the direction of field is .............. \(J\)