A hole is drilled in a metal sheet. At $27^{\circ}\,C$, the diameter of hole is $5\,cm$. When the sheet is heated to $177^{\circ}\,C$, the change in the diameter of hole is $d \times$ $10^{-3}\,cm$. The value of $d$ will be $...........$ if coefficient of linear expansion of the metal is $1.6 \times$ $10^{-5} /{ }^{\circ}\,C$

If two rods of length $L$ and $2L$ having coefficients of linear expansion $\alpha$ and $2\alpha$ respectively are connected so that total length becomes $3L$, the average coefficient of linear expansion of the composition rod equals:

Each side of a box made of metal sheet in cubic shape is $'a'$ at room temperature $'T'$, the coefficient of linear expansion of the metal sheet is $^{\prime} \alpha^{\prime}$. The metal sheet is heated uniformly, by a small temperature $\Delta T$, so that its new temperature is $T +\Delta T$. Calculate the increase in the volume of the metal box.

$5$ litre of benzene weighs

The coefficient of volumetric expansion of mercury is $18 × 10^{-5}{°C^{-1}}$. A thermometer bulb has a volume $10^{-6}\, m^3$ and cross section of stem is $ 0.004 \,cm^2$. Assuming that bulb is filled with mercury at $0°C$ then the length of the mercury column at $100°C$ 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 $=1.20 \times 10^{-5}\; K ^{-1}$