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\(\left.=1.6 \times 10^{-27 /} \ \mathrm{kg}\right)\)

A sphere of capacitance \(100\) pF is charged to a potential of \(100\) V. Another identical uncharged metal sphere is brought in contact with the charged sphere, then the change in the total energy stored on these spheres, when they touch is \(\alpha \times 10^{-7}\) J. The value of \(\alpha\) is __________. (combined capacitance of spheres is \(200\) pF)

A parallel plate capacitor of capacitance \(12.5 \mathrm{pF}\) is charged by a battery connected between its plates to potential difference of \(12.0 \mathrm{~V}\). The battery is now disconnected and a dielectric slab \(\left(\epsilon_{\mathrm{r}}=6\right)\) is inserted between the plates. The change in its potential energy after inserting the dielectric slab is _______.\(\times 10^{-12} \mathrm{~J}\).

If \({q}_{{f}}\) is the free charge on the capacitor plates and \({q}_{{b}}\) is the bound charge on the dielectric slab of dielectric constant \(k\) placed between the capacitor plates, then bound charge \(q_{b}\) can be expressed as 

The current flowing through the \(1 \Omega\) resistor is \(\frac{\mathrm{n}}{10} \ A.\) The value of \(n\) is _______.

The radius of \(2^{\text {nd }}\) orbit of \(He ^{+}\)of Bohr's model is \(r _1\) and that of fourth orbit of \(Be ^{3+}\) is represented as \(r _2\). Now the ratio \(\frac{r_2}{r_1}\) is \(x : 1\). The value of \(x\) is .........

A cube of ice floats partly in water and partly in kerosene oil. The ratio of volume of ice immersed in water to that in kerosene oil is _______.(specific gravity of Kerosene oil \(=0.8\), specific gravity of ice \(=0.9\) )

If the potential barrier across a \(p - n\) junction is \(0.6\,V\). Then the electric field intensity, in the depletion region having the width of \(6 \times 10^{-6} m\), will be \(......\times 10^{5} N / C\).

The current \(I_{1}\) (in \(A\)) flowing through \(1\; \Omega\) resistor in the following circuit is:

In the diagram shown, the difference in the two tubes of the manometer is \(5\, cm\), the cross section of the tube at \(A\) and \(B\) is \(6\, mm^2\) and \(10\, mm^2\) respectively. The rate at which water flows through the tube is ........ \( cc/s\) \((g\, = 10\, ms^{-2})\)

\(\mathrm{A}, \mathrm{B}\) and C are disc, solid sphere and spherical shell respectively with same radii and masses. These masses are placed as shown in figure.

The moment of inertia of the given system about \(P Q\) is \(\frac{X}{15} I\), where \(I\) is the moment of inertia of the disc about its diameter. The value of x is _______.

Two balls of same mass and carrying equal charge are hung from a fixed support of length \(l\). At electrostatic equilibrium, assuming that angles made by each thread is small, the separation, \(x\) between the balls is proportional to

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.