Two metal rods $A$ and $B$ each of length $50 \ cm$ and diameter $4.0 \ mm$ are joined together at temperature $30^{\circ} C$. What is the change in length of the combined rod at $230^{\circ} C$ (in $mm$)? [Given linear expansion coefficients of rods $A$ and $B$ are respectively, $2.0 \times 10^{-5} /^{\circ} C$ and $1.0 \times 10^{-5} /^{\circ} C$]

$A$ cylindrical metal rod of length $L_0$ is shaped into a ring with a small gap $x$ as shown. On heating the system:

Two rods,one of aluminium and the other 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 of aluminium and steel are $\alpha_1$ and $\alpha_2$ respectively. If the length of each rod increases by the same amount,when their temperatures are raised by $t^{\circ}C$,then the ratio $\frac{L_1}{L_1+L_2}$ will be

$A$ glass flask contains some mercury at room temperature. It is found that at different temperatures the volume of air inside the flask remains the same. If the volume of mercury in the flask is $300 \, cm^3$,then the volume of the flask is ........ $cm^3$. (Given that the coefficient of volume expansion of mercury is $\gamma_{Hg} = 1.8 \times 10^{-4} (^{\circ}C)^{-1}$ and the coefficient of linear expansion of glass is $\alpha_{glass} = 9 \times 10^{-6} (^{\circ}C)^{-1}$)

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

$A$ clock pendulum made of invar has a period of $0.5 \, s$ at $20^{\circ} C$. If the clock is used in a climate where the temperature averages to $30^{\circ} C$, how much time does the clock lose in each oscillation? (For invar, $\alpha = 9 \times 10^{-7} /{ }^{\circ} C$, $g = \text{constant}$)