The coefficient of linear expansion of brass and steel rods are $\alpha_1$ and $\alpha_2$. Lengths of brass and steel rods are $L_1$ and $L_2$ respectively. If $(L_2-L_1)$ remains the same at all temperatures, which one of the following relations holds good?
1. $\alpha_1L_2^2=\alpha_2L_1^2$
2. $\alpha_1^2L_2=\alpha_2^2L_1$
3. $\alpha_1L_1=\alpha_2L_2$
4. $\alpha_1L_2=\alpha_2L_1$

The coefficient of area expansion $\beta$ of a rectangular sheet of a solid in terms of the coefficient of linear expansion $\alpha$ is:
1. $2\alpha$
2. $\alpha$
3. $3\alpha$
4. $\alpha^2$

A rod $\mathrm{A}$ has a coefficient of thermal expansion $(\alpha_A)$ which is twice of that of rod $\mathrm{B}$ $(\alpha_B)$. The two rods have length $l_A,~l_B$ where $l_A=2l_B$. If the two rods were joined end-to-end, the average coefficient of thermal expansion is:

The temperature of water at the surface of a deep lake is $2^{\circ} ~\text{C}.$ The temperature expected at the bottom is:
1. $0^{\circ} \mathrm{C}$
2. $2^{\circ} \mathrm{C}$
3. $4^{\circ} \mathrm{C}$
4. $6^{\circ} \mathrm{C}$