$A$ rod of length $2 \ m$ rests on a smooth horizontal floor. If the rod is heated from $0^\circ C$ to $20^\circ C$, find the longitudinal thermal strain developed? $(\alpha = 5 \times 10^{-5} / ^\circ C)$

$A$ hole of diameter $5 \ cm$ is drilled in a metal sheet at $30^{\circ} C$. The coefficient of linear expansion of the metal is $2 \times 10^{-5} K^{-1}$. The diameter of the hole when the temperature is raised to $230^{\circ} C$ is equal to: (in $cm$)

The length of a metal rod at $30^{\circ} C$ is $30 \ cm$. If its temperature is raised to $105^{\circ} C$, its length is increased by $0.027 \ cm$. Then the coefficient of linear expansion of the metal is

$A$ steel tape gives correct measurement at $20^{\circ} C$. $A$ piece of wood is being measured with the steel tape at $0^{\circ} C$. The reading is $25 \ cm$ on the tape. The real length of the given piece of wood must be:

Two wires $A$ and $B$ of the same length,same area of cross-section,and having the same Young's modulus are heated to the same temperature range. If the coefficient of linear expansion of wire $A$ is $3/2$ times that of wire $B$,what is the ratio of the thermal forces produced in the two wires?

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 $(l_2 - l_1)$ is maintained same at all temperatures,which one of the following relations holds good?