If \(10^{22}\) gas molecules each of mass \(10^{-26}\, kg\) collide with a surface (perpendicular to it)elastically per second over an area \(1\, m^2\) with a speed \(10^4\,m/s\), the pressure exerted by the gas molecules will be of the order of

Taking the wavelength of first Balmer line in hydrogen spectrum (\( n = 3\) to \(n = 2\) ) as \(660\,nm ,\) the wavelength of the \(2^{nd}\) Balmer line ( \(n =4\) to \(n = 2\) ) will be....\(nm\)

A plane electromagnetic wave travels in a medium of relative permeability \(1.61\) and relative permittivity \(6.44\). If magnitude of magnetic intensity is \(4.5 \times 10^{-2} \;Am ^{-1}\) at a point, what will be the approximate magnitude of electric field intensity at that point\(?\) (Given : permeability of free space \(\mu_{0}=4 \pi \times 10^{-7}\;NA ^{-2}\), speed of light in vacuum \(c =3 \times 10^{8} \;ms ^{-1}\) )

The engine of a train moving with speed \(10\,ms ^{-1}\) towards a platform sounds a whistle at frequency \(400\,Hz\). The frequency heard by a passenger inside the train is \(........\,Hz\) (neglect air speed. Speed of sound in air \(330\,ms ^{-1}\) )

The speed of a longitudinal wave in a metallic bar is \(400~m/s.\) If the density and Young's modulus of the bar material are increased by 0.5% and 1% respectively then the speed of the wave is changed approximately to ___________ \(m / s\).

A heat engine operates between a cold reservoir at temperature \({T}_{2}=400\, {K}\) and a hot reservoir at temperature \({T}_{1} .\) It takes \(300 \,{J}\) of heat from the hot reservoir and delivers \(240\, {J}\) of heat to the cold reservoir in a cycle. The minimum temperature of the hot reservoir has to be \(....{K}\)

Radiation coming from transition \(n = 2\) to \(n = 1\) of hydrogen atoms fall of \(He^+\) ions in \(n = 1\) and \(n = 2\) states. The possible. Transition of helium ions as they absorb energy from the radiation is

A hollow sphere is rolling on a plane surface about its axis of symmetry. The ratio of rotational kinetic energy to its total kinetic energy is \(\frac{x}{5}\). The value of \(x\) is _______.

Two stars of masses \(m\) and \(2\, m\) at a distance \(d\) rotate about their common centre of mass in free space. The period of revolution is

Two identical parallel plate capacitors, of capacitance \(C\) each, have plates of area \(A\), separated by a distance \(d\). The space between the plates of the two capacitors, is filled with three dielectrics, of equal thickness and dielectric constants \(K_1\) , \(K_2\) and \(K_3\) . The first capacitor is filled as shown in fig. \(I\), and the second one is filled as shown in fig. \(II\). If these two modified capacitors are charged by the same potential \(V\), the ratio of the energy stored in the two, would be ( \(E_1\) refers to capacitor \((I)\) and \(E_2\) to capacitor \((II)\)) 

A plane is in level flight at constant speed and each of its two wings has an area of \(40 \mathrm{~m}^2\). If the speed of the air is \(180 \mathrm{~km} / \mathrm{h}\) over the lower wing surface and \(252 \mathrm{~km} / \mathrm{h}\) over the upper wing surface, the mass of the plane is _______ \(\mathrm{kg}\). (Take air density to be \(1 \mathrm{~kg} \mathrm{~m}^{-3}\) and \(\mathrm{g}=10 \mathrm{~ms}^{-2}\) )