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........$^{\circ}C$.

Thermal expansion of a solid is due to the

$A$ 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.

$A$ rod of length $20 \, cm$ is made of metal $A$. It expands by $0.075 \, cm$ when its temperature is raised from $0^{\circ}C$ to $100^{\circ}C$. Another rod of a different metal $B$ having the same length expands by $0.045 \, cm$ for the same change in temperature. $A$ third rod of the same length is composed of two parts,one of metal $A$ and the other of metal $B$. This rod expands by $0.06 \, cm$ for the same change in temperature. The portion made of metal $A$ has the length ............. $cm$.

The length of a steel rod is $5 \ cm$ longer than a copper rod at all temperatures. What are the lengths of the steel and copper rods? (The coefficients of linear expansion for steel and copper are $1.1 \times 10^{-5} /{ }^{\circ} C$ and $1.7 \times 10^{-5} /{ }^{\circ} C$,respectively.)

The coefficients of linear expansion of brass and steel are ${\alpha _1}$ and ${\alpha _2}$ respectively. If we take a brass rod of length ${l_1}$ and a steel rod of length ${l_2}$ at $0^{\circ}C$,their difference in length $({l_2} - {l_1})$ will remain the same at any temperature if: