The temperature of a wire of length $1 \, m$ and area of cross-section $1 \, cm^2$ is increased from $0^\circ C$ to $100^\circ C$. If the rod is not allowed to increase in length,the force required will be $(\alpha = 10^{-5} /^\circ C$ and $Y = 10^{11} \, N/m^2)$.

$A$ 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 .......... $cm$.

To increase the length of a metal rod by $0.4 \%$,the temperature of the rod is to be increased by (Coefficient of linear expansion of the metal $= 20 \times 10^{-6} \ {}^{\circ}C^{-1}$) (in $K$)

Railway tracks are made of steel segments separated by small gaps to allow for linear expansion. $A$ segment of the track is $10 \ m$ long when laid at a temperature of $17^{\circ} C$. The maximum temperature that can be reached is $45^{\circ} C$. The increase in the length of the segment of the railway track is $x \times 10^{-5} \ m$. The value of $x$ is (given $\alpha_{\text{steel}} = 1.2 \times 10^{-5} /{ }^{\circ} C$).

Two holes of unequal diameters $d_1$ and $d_2$ $(d_1 > d_2)$ are cut in a metal sheet. If the sheet is heated,then:

Assertion :- $A$ brass disc is fast fitted in a hole in a steel plate. The system must be cooled to loosen the disc from the hole.
Reason :- The coefficient of linear expansion of brass is greater than the coefficient of linear expansion of steel.