The focal length of a spherical mirror made of steel is $150 \,cm$. If the temperature of the mirror increases by $200 \,K$, its focal length becomes (coefficient of linear expansion of steel $\alpha = 12 \times 10^{-6} \,^{\circ}C^{-1}$). (in $\,cm$)

The linear expansion coefficients of brass and steel wires are $\alpha_1$ and $\alpha_2$ respectively,and their lengths at $0^\circ C$ are $L_1$ and $L_2$. If the difference $(L_2 - L_1)$ remains constant at any temperature,then:

Two large holes are cut in a metal sheet. If this sheet is heated,what happens to the distances $AB$ and $BC$ as shown in the figure?

The density of a substance at $0 \, ^\circ C$ is $10 \, g/cm^3$ and at $100 \, ^\circ C$ is $9.7 \, g/cm^3$. The coefficient of linear expansion of the substance is ..... $^\circ C^{-1}$.

$A$ uniform metal rod of length $L$ and mass $M$ is rotating about an axis passing through one of the ends and perpendicular to the rod with angular speed $\omega$. If the temperature increases by $t^{\circ} C$, then the change in its angular velocity is proportional to which of the following? (Coefficient of linear expansion of rod $= \alpha$)

$A$ sheet of steel is $40 \ cm$ long and $5 \ cm$ broad at $0^{\circ} C$. The surface area of the sheet increases by $1.4 \ cm^2$ at $100^{\circ} C$. The coefficient of linear expansion of steel is: