A monoatomic ideal gas initially at temperature '$$\mathrm{T}_1$$' is enclosed in a cylinder fitted with massless, frictionless piston. By releasing the piston suddenly the gas is allowed to expand to adiabatically to a temperature '$$\mathrm{T}_2$$'. If '$$\mathrm{L}_1$$' and '$$\mathrm{L}_2$$' are the lengths of the gas columns before and after expansion respectively, then $$\frac{\mathrm{T}_2}{\mathrm{~T}_1}$$ is

A tuning fork of frequency $$220 \mathrm{~Hz}$$ produces sound waves of wavelength $$1.5 \mathrm{~m}$$ in air at N.T.P. The increase in wavelength when the temperature of air is $$27^{\circ} \mathrm{C}$$ is nearly $$\left(\sqrt{\frac{300}{273}}=1.05\right)$$

An air craft of wing span $$40 \mathrm{~m}$$ files horizontally in earth's magnetic field $$5 \times 10^{-5} \mathrm{~T}$$ at a speed of $$500 \mathrm{~m} / \mathrm{s}$$. The e.m.f. generated between the tips of the wings of the air craft is

In $$\mathrm{P}^{\text {th }}$$ second, a particle describes angular displacement of '$$\beta$$' rad. If it starts from rest, the angular acceleration is