A hemispherical vessel is completely filled with a liquid of refractive index \(\mu\). A small coin is kept at the lowest point \((\mathrm{O})\) of the vessel as shown in figure. The minimum value of the refractive index of the liquid so that a person can see the coin from point E (at the level of the vessel) is _______.

If Rydberg's constant is \(R\), the longest wavelength of radiation in Paschen series will be \(\frac{\alpha}{7 R}\), where \(\alpha=\)____________

Identify the characteristics of an adiabatic process in a monoatomic gas.
(A) Internal energy is constant.
(B) Work done in the process is equal to the charge in internal energy.
(C) The product of temperature and volume is a constant.
(D) The product of pressure and volume is a constant.
(E) The work done to change the temperature from \(\mathrm{T}_1\) to \(\mathrm{T}_2\) is proportional to \(\left(\mathrm{T}_2-\mathrm{T}_1\right)\)
Choose the correct answer from the options given below :

A light unstretchable string passing over a smooth light pulley connects two blocks of masses \(m_1\) and \(m_2\). If the acceleration of the system is \(\frac{g}{8}\), then the ratio of the masses \(\frac{\mathrm{m}_2}{\mathrm{~m}_1}\) is _______.

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.

In a single slit diffraction pattern, a light of wavelength \(6000\) A is used. The distance between the first and third minima in the diffraction pattern is found to be \(3 \mathrm{~mm}\) when the screen in placed 50 \(\mathrm{cm}\) away from slits. The width of the slit is _______ \(\times 10^{-4} \mathrm{~m}\).

Consider a planet in some solar system which has a mass double the mass of earth and density equal to the average density of earth. If the weight of an object on earth is \({W}\), then weight of the same object on that planet will be

A monoatomic gas at pressure \(P\) and volume \(V\) is suddenly compressed to one eighth of its original volume. The final pressure at constant entropy will be \(.....P\)

This questions has Statement \(I\) and Statement \(II\) Of the four choices given after the Statements, choose the one that best describes into two Statements.
Statement\(-I\) : Higher the range, greater is the resistance of ameter.
Statement\(-II\) : To increase the range of ammeter, additional shunt needs to be used across it.

Assume that the displacement\((s)\) of air is proportional to the pressure difference \((\Delta p)\) created by a sound wave. Displacement\((s)\) further depends on the speed of sound \((v),\) density of air \((\rho)\) and the frequency \((f)\) If \(\Delta p \approx 10\, Pa , v  \approx 300\, m / s , p  \approx 1\, kg / m ^{3}\) and \(f \approx  1000 \,Hz\), then \(s\) will be the order of (take multiplicative constant to be \(1\) )

In an adiabatic process, which of the following statements is true?