$$1 \mathrm{~kg}$$ of water at $$100^{\circ} \mathrm{C}$$ is converted into steam at $$100^{\circ} \mathrm{C}$$ by boiling at atmospheric pressure. The volume of water changes from $$1.00 \times 10^{-3} \mathrm{~m}^{3}$$ as a liquid to $$1.671 \mathrm{~m}^{3}$$ as steam. The change in internal energy of the system during the process will be

(Given latent heat of vaporisaiton $$=2257 \mathrm{~kJ} / \mathrm{kg}$$, Atmospheric pressure = $$\left.1 \times 10^{5} \mathrm{~Pa}\right)$$

The critical angle for a denser-rarer interface is $$45^{\circ}$$. The speed of light in rarer medium is $$3 \times 10^{8} \mathrm{~m} / \mathrm{s}$$. The speed of light in the denser medium is:

On a temperature scale '$$\mathrm{X}$$', the boiling point of water is $$65^{\circ} \mathrm{X}$$ and the freezing point is $$-15^{\circ} \mathrm{X}$$. Assume that the $$\mathrm{X}$$ scale is linear. The equivalent temperature corresponding to $$-95^{\circ} \mathrm{X}$$ on the Farenheit scale would be:

The radii of two planets 'A' and 'B' are 'R' and '4R' and their densities are $$\rho$$ and $$\rho / 3$$ respectively. The ratio of acceleration due to gravity at their surfaces $$\left(g_{A}: g_{B}\right)$$ will be: