The electric potential at the surface of an atomic nucleus \((Z=50)\) of radius \(9 \times 10^{-13} cm\) is \(\alpha \times 10^6 V\). What is the value of \(\alpha\)?
(Charge of proton \(1.6 \times 10^{-19} C\) )

A tank with a small hole at the bottom has been filled with water and kerosene (specific gravity \(0.8\)). The height of water is \(3\,m\) and that of kerosene \(2\,m\). When the hole is opened the velocity of fluid coming out from it is nearly ........ \(ms^{-1}\) .(take \(g\, = 10\, m s^{-2}\) and density of water \(= 10^3\, kg\, m^{-3}\))

In an electrical circuit, a battery is connected to pass \(20\, C\) of charge through it in a certain given time. The potential difference between two plates of the battery is maintained at \(15\, V\). The work done by the battery is ........... \(J\).

A zener diode having zener voltage \(8\, {V}\) and power dissipation rating of \(0.5\, {W}\) is connected across a potential divide arranged with maximum potential drop across zener diode is as shown in the diagram. The value of protective resistance \({R}_{{p}}\) is \(....\,\Omega\)

Two resistors are connected in series across a battery as shown in figure. If a voltmeter of resistance \(2000 \,\Omega\) is used to measure the potential difference across \(500 \,\Omega\) resister, the reading of the voltmeter will be ............... \(V\)

The activity of a radioactive sample falls from \(700 \;\mathrm{s}^{-1}\) to \(500\; \mathrm{s}^{-1}\) in \(30\;min\). Its half life is close to.........\(min\)

An ideal gas initially at \(0^{\circ} \mathrm{C}\) temperature, is compressed suddenly to one fourth of its volume. If the ratio of specific heat at constant pressure to that at constant volume is \(3 / 2\), the change in temperature due to the thermodynamic process is _____ K.

The mass of a hydrogen molecule is \(3.32 \times 10^{-27 } \) \(kg\). If \(10^{23}\) hydrogen molecules strike, per second, a fixed wall of area \(2\) \(cm^2\) at an angle of \(45^o \) to the normal, and rebound elastically with a speed of \(10^3\ m/s\), then the pressure on the wall is nearly:

A nucleus of mass \(M\) at rest splits into two parts having masses \(\frac{M^{\prime}}{3}\) and \(\frac{2 M^{\prime}}{3}\left(M^{\prime} < M\right)\). The ratio of de Broglie wavelength of two parts will be.

Two open organ pipes of length \(60 \mathrm{~cm}\) and \(90 \mathrm{~cm}\) resonate at \(6^{\text {th }}\) and \(5^{\text {th }}\) harmonics respectively. The difference of frequencies for the given modes is _______ \(\mathrm{Hz}\). (Velocity of sound in air \(=333 \mathrm{~m} / \mathrm{s}\) )