A diatomic gas $$\left(\gamma=\frac{7}{5}\right)$$ is compressed adiabatically to volume $$\frac{V_i}{32}$$ where $$V_i$$ is its initial volume. The initial temperature of the gas is $$T_i$$ in Kelvin and the final temperature is '$$x T_i$$'. The value of '$$x$$' is

A disc has mass $$M$$ and radius $$R$$. How much tangential force should be applied to the rim of the disc, so as to rotate with angular velocity '$$\omega$$' in time $$\mathrm{t}$$ ?

An electron moving with velocity $$1.6 \times 10^7 \mathrm{~m} / \mathrm{s}$$ has wavelength of $$0.4 \mathop A\limits^o$$. The required accelerating voltage for the electron motion is [charge on electron $$=1.6 \times 10^{-19} \mathrm{C}$$, mass of electron $$=9 \times 10^{-31} \mathrm{~kg}$$ ]

The prism has refracting angle '$$\mathrm{A}$$'. The second refracting surface of the prism is silvered. Light ray falling on first refracting surface with angle of incidence '$$2 \mathrm{~A}$$', reaches the second surface and returns back through the same path due to reflection at the silvered surface. The refractive index of the material of the prism is