To increase the length of a metal rod by $0.4 \%$,the temperature of the rod is to be increased by (Coefficient of linear expansion of the metal $= 20 \times 10^{-6} \ {}^{\circ}C^{-1}$) (in $K$)

An equilateral triangle $ABC$ is formed by two copper rods $AB$ and $BC$ and one aluminium rod $AC$. The system is heated such that the temperature of each rod increases by $\Delta T$. Find the change in the angle $\angle ABC$. (Coefficient of linear expansion for copper is $\alpha_1$ and for aluminium is $\alpha_2$).

On what value does the coefficient of linear expansion $\alpha_l$ depend? Write its unit.

At some temperature $T$,a bronze pin is slightly too large to fit into a hole drilled in a steel block. The change in temperature required for an exact fit is minimum when:

What must be the lengths of steel and copper rods at $0^o C$ for the difference in their lengths to be $10\,cm$ at any common temperature? $(\alpha_{steel}=1.2 \times 10^{-5} \;^o C^{-1})$ and $(\alpha_{copper} = 1.8 \times 10^{-5} \;^o C^{-1})$

$A$ metal ball initially at a pressure of $10^5 \ Pa$ is heated from $20^{\circ} C$ to $127^{\circ} C$ while keeping its volume constant. The coefficient of linear expansion of the metal is $10^{-5} \ {^{\circ} C}^{-1}$ and the bulk modulus of the metal is $2 \times 10^{11} \ N \ m^{-2}$. The final pressure inside the ball becomes: