A crystal has a coefficient of expansion $13\times10^{-7}$ in one direction and $231\times10^{-7}$ in every direction at right angles to it. Then the cubical coefficient of expansion is

A rod of length $l$ and radius $r$ is held between two rigid walls so that it is not allowed to expand. If its temperature is increased, then the force developed in it is proportional to .........

A solid metallic cube having total surface area $24\;m ^{2}$ is uniformly heated. If its temperature is increased by $10\,^{\circ} C$, calculate the increase in volume of the cube $\left(\right.$ Given $\left.: \alpha=5.0 \times 10^{-4}{ }^{\circ} C ^{-1}\right)$

When the temperature of a metal wire is increased from $0^{\circ} \,C$ to $10^{\circ}\, C$, its length increases by $0.02 \% .$ The percentage change in its mass density will be closest to:

Water falls from a height $500m$. What is the rise in temperature of water at bottom if whole energy remains in the water ........... $^\circ \mathrm{C}$

A vertical column $50$ $cm$ long at $50°C$ balances another column of same liquid $60 \,cm$ long at $100°C$. The coefficient of absolute expansion of the liquid is