The workdone by a gas molecule in an isolated system is given by, \(W =\alpha \beta^{2} e ^{-\frac{ x ^{2}}{\alpha kT }},\) where \(x\) is the displacement, \(k\) is the Boltzmann constant and \(T\) is the temperature, \(\alpha\) and \(\beta\) are constants. Then the dimension of \(\beta\) will be

A wire of resistance \(160\,\Omega\) is melted and drawn in wire of one-fourth of its length. The new resistance of the wire will be \(......\Omega\)

Considering Bohr's atomic model for hydrogen atom :
(A) the energy of H atom in ground state is same as energy of \(\mathrm{He}^{+}\)ion in its first excited state.
(B) the energy of H atom in ground state is same as that for \(\mathrm{Li}^{++}\)ion in its second excited state.
(C) the energy of H atom in its ground state is same as that of \(\mathrm{He}^{+}\)ion for its ground state.
(D) the energy of \(\mathrm{He}^{+}\)ion in its first excited state is same as that for \(\mathrm{Li}^{++}\)ion in its ground state
Choose the correct answer from the options given below :

A parallel plate capacitor of capacitance \(1 \mu \mathrm{~F}\) is charged to a potential difference of 20 V . The distance between plates is \(1 \mu \mathrm{~m}\). The energy density between plates of capacitor is _________.

Match List \(I\) with List \(II\)

List \(I\)	List \(II\)
\((A)\) Young's Modulus \((Y)\)	\((I)\) \(\left[ M L ^{-1} T ^{-1}\right]\)
\((B)\) Co-efficient of Viscosity \((\eta)\)	\((II)\) \(\left[ M L ^2 T ^{-1}\right]\)
\((C)\) Planck's Constant \((h)\)	\((III)\) \(\left[ M L ^{-1} T ^{-2}\right]\)
\((D)\) Work Function \((\phi)\)	\((IV)\) \(\left[ M L ^2 T ^{-2}\right]\)

Choose the correct answer from the options given below:

10 mole of an ideal gas is undergoing the process shown in the figure. The heat involved in the process from \(P _1\) to \(P _2\) is \(\alpha\) Joule \(\left( P _1=21.7 Pa\right.\) and \(\left.P _2=30 Pa, C _{ v }=21 J / K . mol , R=8.3 J / mol . K \right)\). The value of \(\alpha\) is _________ .

In a photoelectric effect experiment a light of frequency \(1.5\) times the threshold frequency is made to fall on the surface of photosensitive material. Now if the frequency is halved and intensity is doubled, the number of photo electrons emitted will be _______.

A flask contains argon and oxygen in the ratio of \(3: 2\) in mass and the mixture is kept at \(27^{\circ} C\). The ratio of their average kinetic energy per molecule respectively will be ...........

Three objects \(A, B\) and \(C\) are kept in a straight line on a frictionless horizontal surface. The masses of \({A}, {B}\) and \({C}\) are \({m}, 2\, {m}\) and \(2\, {m}\) respectively. \(A\) moves towards \({B}\) with a speed of \(9\) \({m} / {s}\) and makes an elastic collision with it. Thereafter \(B\) makes a completely inelastic collision with \(C.\) All motions occur along same straight line. The final speed of \(C\) is \(....\,{m} / {s}\)