An insulated cylinder of volume \( 60\,cm^{3} \) is filled with a gas at \( 27^{\circ}C \) and 2 atmospheric pressure. Then the gas is compressed making the final volume as \( 20\,cm^{3} \) while allowing the temperature to rise to \( 77^{\circ}C \). The final pressure is __________atmospheric pressure.

The terminal velocity of a metallic ball of radius 6 mm in a viscous fluid is \(20 cm / s\). The terminal velocity of another ball of same material and having radius 3 mm in the same fluid will be _________ \(cm / s\).

The radius of electron's second stationary orbit in Bohr's atom is \(R\). The radius of the third orbit will be

A mixture of one mole of monoatomic gas and one mole of a diatomic gas (rigid) are kept at room temperature \(\left(27^{\circ} \mathrm{C}\right)\). The ratio of specific heat of gases at constant volume respectively is _______.

In an experiment of measuring the refractive index of a glass slab using travelling microscope in physics lab, a student measures real thickness of the glass slab as \(5.25\,mm\) and apparent thickness of the glass slab at \(5.00\,mm\). Travelling microscope has \(20\) divisions in one \(cm\) on main scale and \(50\) divisions on Vernier scale is equal to \(49\) divisions on main scale. The estimated uncertainty in the measurement of refractive index of the slab is \(\frac{x}{10} \times 10^{-3}\), where \(x\) is \(..............\)

A uniform rectangular thin sheet \(ABCD\) of mass \(M\) has length \(a\) and breadth \(b\), as shown in the figure. If the shaded portion \(HBGO\) is cut off, the coordinates of the centre of mass of the remaining portion will be

A point source of light is placed at the centre of curvature of a hemispherical surface. The source emits a power of \(24\,W\) The radius of curvature of hemisphere is \(10\,cm\) and the inner surface is completely reflecting. The force on the hemisphere due to the light falling on it is \(..........\times 10^{-8}\,N\).

Two coherent sources of light interfere. The intensity ratio of two sources is \(1: 4\). For this interference pattern if the value of \(\frac{I_{\max }+I_{\min }}{I_{\max _{\max }}-I_{\min }}\) is equal to \(\frac{2 \alpha+1}{\beta+3}\), then \(\frac{\alpha}{\beta}\) will be.

Zener breakdown occurs in a \(p-n\) junction having \(p\) and \(n\) both :

A metal surface is illuminated by a radiation of wavelength \(4500 \; \mathring A\). The ejected photo-electron enters a constant magnetic field of \(2 \; mT\) making an angle of \(90^{\circ}\) with the magnetic field. If it starts revolving in a circular path of radius \(2 \; mm\), the work function of the metal is approximately ............. \(eV\)