The coefficient of apparent expansion of a liquid when determined using two different vessels $A$ and $B$ are $\gamma_1$ and $\gamma_2$ respectively. If the coefficient of linear expansion of vessel $A$ is $\alpha$, the coefficient of linear expansion of vessel $B$ is

- A
$\frac{{\alpha {\gamma _1}{\gamma _2}}}{{{\gamma _1} + {\gamma _2}}}$

- B
$\frac{{{\gamma _1} - {\gamma _2}}}{{2\alpha }}$

- C
$\frac{{{\gamma _1} - {\gamma _2} + \alpha }}{3}$

- D
$\frac{{{\gamma _1} - {\gamma _2}}}{3} + \alpha $

The volume of a metal sphere increases by $0.24\%$ when its temperature is raised by $40°C$. The coefficient of linear expansion of the metal is .......... $°C$

A thin rod having length $L_0$ at $0\,^oC$ and coefficient of linear expansion $\alpha $ has its two ends maintained at temperatures $\theta _1$ and $\theta _2$, respectively. Find its new length.

An iron bar of length $10\, m$ is heated from $0°C$ to $100°C.$ If the coefficient of linear thermal expansion of iron is $ 10 \times 10^{-6}{°C^{-1}}$, the increase in the length of bar is .......... $cm$

A pendulum clock keeps correct time at $0°C$. Its mean coefficient of linear expansions is $\alpha /^\circ C$, then the loss in seconds per day by the clock if the temperature rises by $t°C$ is

A steel tape $1 \;m$ long is correctly calibrated for a temperature of $27.0\,^{\circ} C .$ The length of a steel rod measured by this tape is found to be $63.0 \;cm$ on a hot day when the temperature is $45.0\,^{\circ} C .$ What is the actual length of the steel rod on that day ? What is the length of the same steel rod on a day when the temperature is $27.0\,^oC$? Coefficient of linear expansion of steel $=1.20 \times 10^{-5}\; K ^{-1}$