The coefficient of linear expansion of a crystalline substance in one direction is $2 \times 10^{-4} /{ }^{\circ} C$ and in every direction perpendicular to it is $3 \times 10^{-4} /{ }^{\circ} C$. The coefficient of cubical expansion of the crystal is equal to ........... $\times 10^{-4} /{ }^{\circ} C$.

$A$ metal tape is calibrated at $25^{\circ} C$. On a cold day when the temperature is $-15^{\circ} C$,the percentage error in the measurement of length is (Coefficient of linear expansion of metal $= 1 \times 10^{-5} {}^{\circ} C^{-1}$) (in $\%$)

The rods of length $L_1$ and $L_2$ are made of materials whose coefficients of linear expansion are $\alpha_1$ and $\alpha_2$ respectively. If the difference between the two lengths is independent of temperature,then:

When the temperature of a metal sphere is increased by $40^{\circ}C$,its volume increases by $0.24\%$. The coefficient of linear expansion of the metal is ....... $^{\circ}C^{-1}$.

$A$ seconds pendulum clock has a steel wire. The clock shows correct time at $25^{\circ} C$. How many seconds does the clock lose or gain in one week,when the temperature is increased to $35^{\circ} C$? (Given: $\alpha_{\text{steel}} = 1.2 \times 10^{-5} /^{\circ} C$)

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