$A$ clock with an iron pendulum keeps correct time at $15^{\circ} C$. If the room temperature is $20^{\circ} C$,the error in seconds per day will be nearly (coefficient of linear expansion of iron is $\alpha = 1.2 \times 10^{-5} /{ }^{\circ} C$) (in $s$)

Two rods $A$ and $B$ of identical dimensions are at temperature $30\,^{\circ}C$. If $A$ is heated up to $180\,^{\circ}C$ and $B$ up to $T\,^{\circ}C$,then the new lengths are the same. If the ratio of the coefficients of linear expansion of $A$ and $B$ is $4:3$,then the value of $T$ is........$^{\circ}C$.

$A$ thin rod having length $L_0$ at $0\,^{\circ}C$ and coefficient of linear expansion $\alpha$ has its two ends maintained at temperatures $\theta_1$ and $\theta_2$,respectively. Find its new length.

$A$ bar of iron is $10 \, cm$ at $20^{\circ}C$. At $19^{\circ}C$ it will be ($\alpha$ of iron $= 11 \times 10^{-6}/^{\circ}C$)

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A$: When a rod lying freely is heated,no thermal stress is developed in it.
Reason $R$: On heating,the length of the rod increases.
In the light of the above statements,choose the correct answer from the options given below:

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?