Two moles of an ideal monoatomic gas occupies a volume \(V\) at \(27^o C\). The gas expands adiabatically to a volume \(2\ V\). Calculate \((a)\) the final temperature of the gas and \((b)\) change in its internal energy.

Given below are two statements: Statement-\(I\): Figure shows the variation of stopping potential with frequency \((v)\) for the two photosensitive materials \(M_1\) and \(M_2\). The slope gives value of \(\frac{h}{e}\), where \(h\) is Planck's constant, \(e\) is the charge of electron. Statement-\(II\): \(M_2\) will emit photoelectrons of greater kinetic energy for the incident radiation having same frequency. In the light of the above statements, choose the most appropriate answer from the options given below.

Find the electric field at point \(P\) (as shown in figure) on the perpendicular bisector of a uniformly charged thin wire of length \(L\) carrying a charge \(Q.\) The distance of the point \(P\) from the centre of the rod is \(a=\frac{\sqrt{3}}{2} L\).

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 charge stored by the capacitor C in the given circuit in the steady state is _________ \(\mu C\).

A helicopter flying horizontally with a speed of \(360 \mathrm{~km} / \mathrm{h}\) at an altitude of 2 km , drops an object at an instant. The object hits the ground at a point O , 20 s after it is dropped. Displacement of ' O ' from the position of helicopter where the object was released is :
(use acceleration due to gravity \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\) and neglect air resistance)

A particle of mass \(1 \,{mg}\) and charge \(q\) is lying at the mid-point of two stationary particles kept at a distance \('2 \,{m}^{\prime}\) when each is carrying same charge \('q'.\) If the free charged particle is displaced from its equilibrium position through distance \('x'\) \((x\,< \,1\, {m})\). The particle executes \(SHM.\) Its angular frequency of oscillation will be \(....\,\times 10^{8}\, {rad} / {s}\) if \({q}^{2}=10\, {C}^{2}\)

A heavy box of mass \(50 \mathrm{~kg}\) is moving on a horizontal surface. If co-efficient of kinetic friction between the box and horizontal surface is \(0.3\) then force of kinetic friction is _______.

A particle of mass \(9.1 \times 10^{-31}\, {kg}\) travels in a medium with a speed of \(10^{6}\, {m} / {s}\) and a photon of a radiation of linear momentum \(10^{-27} \,{kg}\, {m} / {s}\) travels in vacuum. The wavelength of photon is \(....\) times the wavelength of the particle.

Two metal plates \((A, B)\) are kept horizontally with separation of \(\left(\dfrac{12}{\pi}\right)\) cm, with plate A on the top. An atomizer jet sprays oil (density \(1.5\) g/cm\(^3\)) droplets of radius \(1\) mm horizontally. All oil droplets carry a charge \(5\) nC. The potentials \(V_A\) and \(V_B\) are required on plates A and B respectively in order to ensure the droplets do not descend. The values of \(V_A\) and \(V_B\) are _______.
(Neglect the air resistance to the droplets and take \(g = 10\) m/s\(^2\))

The de-Broglie wavelength of an electron is the same as that of a photon. If velocity of electron is \(25 \%\) of the velocity of light, then the ratio of \(K.E.\) of electron and \(K.E.\) of photon will be:

The excess pressure inside a soap bubble A in air is half the excess pressure inside another soap bubble B in air. If the volume of the bubble A is \(n\) times the volume of the bubble \(B\), then, the value of \(n\) is ___.