The radiation corresponding to \(3 \rightarrow 2\) transition ofhydrogen atom falls on a metal surface to produce photoelectrons. These electrons are made to enter a magnetic field of \(3 \times  10^{-4}\) \(T\) If the radius of the largest circular path followed by these electrons is \(10.0\ mm\), the work function of the metal is close to......\( eV\)

A particle is moving in a circular path of radius \(a,\) with a constant velocity \(v\) as shown in the figure.The centre of circle is marked by \('C'\). The angular momentum from the origin \(O\) can be written as

The temperature of \(3.00\, {mol}\) of an ideal diatomic gas is increased by \(40.0^{\circ} {C}\) without changing the pressure of the gas. The molecules in the gas rotate but do not oscillate. If the ratio of change in internal energy of the gas to the amount of workdone by the gas is \(\frac{{x}}{10} .\) Then the value of \({x}\) (round off to the nearest integer) is ..... . \(\left(\right.\) Given \(\left.{R}=8.31\, {J} {mol}^{-1} {K}^{-1}\right)\)

The elastic behaviour of material for linear streass and linear strain, is shown in the figure. The energy density for a linear strain of \(5 \times 10^{-4}\) is \(\dots \; kJ / m ^{3}\). Assume that material is elastic upto the linear strain of \(5 \times 10^{-4}\).

An \(\alpha\)-particle, a proton and an electron have the same kinetic energy. Which one of the following is correct in case of their De-Broglie wavelength:

For full scale deflection of total \(50\) divisions, \(50\,{mV}\) voltage is required in galvanometer. The resistance of galvanometer if its current sensitivity is \(2\, {div} / {mA}\) will be \(.....\Omega\)

A tuning fork is vibrating at \(250\, {Hz}\). The length of the shortest closed organ pipe that will resonate with the tuning fork will be ..... \({cm}\) (Take speed of sound in air as \(340\, {ms}^{-1}\) )

The internal energy of a monoatomic gas is 3 nRT . One mole of helium is kept in a cylinder having internal cross section area of \(17 cm^2\) and fitted with a light movable frictionless piston. The gas is heated slowly by suppling 126 J heat. If the temperature rises by \(4^{\circ} C\), then the piston will move ___________ cm.
(atmospheric pressure \(=10^5 Pa\) )

If a satellite orbiting the Earth is 9 times closer to the Earth than the Moon, what is the time period of rotation of the satellite? Given rotational time period of Moon \(=27\) days and gravitational attraction between the satellite and the moon is neglected.

A particle executes \(S.H.M.\) of amplitude A along \(x\)-axis. At \(t =0\), the position of the particle is \(x=\frac{A}{2}\) and it moves along positive \(x\)-axis the displacement of particle in time \(t\) is \(x=A \sin (\omega t+\delta)\), then the value \(\delta\) will be

A charged particle carrying charge \(1\,\mu C\) is moving with velocity \((2 \hat{ i }+3 \hat{ j }+4 \hat{ k })\, ms ^{-1} .\) If an external magnetic field of \((5 \hat{ i }+3 \hat{ j }-6 \hat{ k }) \times 10^{-3}\, T\) exists in the region where the particle is moving then the force on the particle is \(\overline{ F } \times 10^{-9} N\). The vector \(\overrightarrow{ F }\) is :

In an experiment of measuring the refractive index of a glass slab using travelling microscope in physics lab, a student measures real thickness of the glass slab as \(5.25\,mm\) and apparent thickness of the glass slab at \(5.00\,mm\). Travelling microscope has \(20\) divisions in one \(cm\) on main scale and \(50\) divisions on Vernier scale is equal to \(49\) divisions on main scale. The estimated uncertainty in the measurement of refractive index of the slab is \(\frac{x}{10} \times 10^{-3}\), where \(x\) is \(..............\)

Match List - I with List - II.

List - I	List - II
A. Boltzmann constant	I. \([M^{-1}L^3T^{-2}]\)
B. Stefan's constant	II. \([ML^2T^{-1}]\)
C. Planck's constant	III. \([ML^2T^{-2}K^{-1}]\)
D. Gravitational constant	IV. \([ML^0T^{-3}K^{-4}]\)

Choose the correct answer from the options given below :