Speed of an electron in Bohr's \(7^{\text {th }}\) orbit for Hydrogen atom is \(3.6 \times 10^6\,m / s\). The corresponding speed of the electron in \(3^{\text {rd }}\) orbit, in \(m / s\) is \(........\times 10^6\)

In the given figure, the face \(AC\) of the equilateral prism is immersed in a liquid of refractive index ' \(n\) '. For incident angle \(60^{\circ}\) at the side \(AC\), the refracted light beam just grazes along face \(AC\). The refractive index of the liquid \(n =\frac{\sqrt{ x }}{4}\). The value of \(x...\) is (Given refractive index of glass \(=1.5\) )

The time taken by an object to slide down \(45^{\circ}\) rough inclined plane is \(n\) times as it takes to slide down a perfectly smooth \(45^{\circ}\) incline plane. The coefficient of kinetic friction between the object and the incline plane is

A tub is filled with water and a wooden cube \(10\) cm \(\times\) \(10\) cm \(\times\) \(10\) cm is placed in the water. The wooden cube is found to float on the water with a part of it submerged in water. When a metal coin is placed on the wooden cube, the submerged part is increased by \(3.87\) cm. The mass of the metal coin is _______ gram.
(Take water density as \(1\) g/cm\(^3\) and density of wood as \(0.4\) g/cm\(^3\))

A body of mass \(8\,kg\) and another of mass \(2\, kg\) are moving with equal kinetic energy. The ratio of their respective momenta will be.

A potentiometer \(PQ\) is set up to compare two resistances as shown in the figure. The ameter \(A\) in the circuit reads \(1.0\, A\) when two way key \(K_3\) is open. The balance point is at a length \(l_1\, cm\) from \(P\) when two way key \(K_3\) is plugged in between \(2\) and \(1\) , while the balance point is at a length \(l_2\, cm\) from \(P\) when key \(K_3\) is plugged in between \(3\) and \(1\) . The ratio of two resistances \(\frac{{{R_1}}}{{{R_2}}}\) is found to be

A concave mirror of focal length \(10\) cm forms an image which is double the size of object when the object is placed at two different positions. The distance between the two positions of the object is __________ cm.

The velocity of sound in air is doubled when the temperature is raised from \(0^{\circ} C\) to \(\alpha^{\circ} C\). The value of \(\alpha\) is ________.

A coil of inductance \(2\, H\) having negligible resistance is connected to a source of supply whose voltage is given by \(V=3 t\) volt. (where \(t\) is in second). If the voltage is applied when \(t =0,\) then the energy stored in the coil after \(4\, s\) is ............ \(J\).

When a hydrogen atom going from \(\mathrm{n}=2\) to \(\mathrm{n}=1\) emits a photon, its recoil speed is \(\frac{\mathrm{x}}{5} \mathrm{~m} / \mathrm{s}\). Where \(\mathrm{x}=\) _______. (Use : mass of hydrogen atom\(\left.=1.6 \times 10^{-27 /} \ \mathrm{kg}\right)\)