$A$ circular metallic disc of radius $R$ has a small circular cavity of radius $r$ as shown in the figure. On heating the system:

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 $\,cm$)

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 $\alpha_{\text{steel}} = 1.2 \times 10^{-5} /{ }^{\circ} C$).

When a copper ball is heated,which of the following will show the maximum percentage increase?

$A$ bar of iron is $10 \, cm$ at $20^{\circ}C$. At $19^{\circ}C$ it will be ($\alpha$ of iron $= 11 \times 10^{-6}/^{\circ}C$)

The difference in length between two rods $A$ and $B$ is $60 \text{ cm}$ at all temperatures. If $\alpha_{A} = 18 \times 10^{-6} /^{\circ}\text{C}$ and $\alpha_{B} = 27 \times 10^{-6} /^{\circ}\text{C}$,the lengths of the two rods are: