$A$ metallic tape gives the correct value at $25^{\circ} C$. $A$ piece of wood is being measured by this metallic tape at $10^{\circ} C$. If the reading is $30 \, cm$ on the tape, the real length of the wooden piece must be .......... $cm$.

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

$A$ steel rod at $25^{\circ} C$ is observed to be $1 \ m$ long when measured by another metal scale which is correct at $0^{\circ} C$. The exact length of the steel rod at $0^{\circ} C$ is $(\alpha_{\text{steel}} = 12 \times 10^{-6} \ ^{\circ} C^{-1}, \alpha_{\text{metal}} = 20 \times 10^{-6} \ ^{\circ} C^{-1})$. (in $m$)

Two rods,one of aluminum and the other made of steel,having initial lengths $l_1$ and $l_2$ are connected together to form a single rod of length $l_1 + l_2$. The coefficients of linear expansion for aluminum and steel are $\alpha_a$ and $\alpha_s$ respectively. If the length of each rod increases by the same amount when their temperature is raised by $t ^\circ C$,then find the ratio $\frac{l_1}{l_1 + l_2}$.

An aluminium sphere of $20 \; cm$ diameter is heated from $0^{\circ} C$ to $100^{\circ} C$. Its volume changes by (given that coefficient of linear expansion for aluminium $\alpha_{Al} = 23 \times 10^{-6} \; /^{\circ} C$): (in $; cm^3$)

The coefficient of apparent expansion of mercury in a glass vessel is $153 \times 10^{-6} \, ^{\circ}C^{-1}$ and in a steel vessel is $144 \times 10^{-6} \, ^{\circ}C^{-1}$. If $\alpha$ for steel is $12 \times 10^{-6} \, ^{\circ}C^{-1}$,then that of glass is: