$A$ solid ball of metal has a concentric spherical cavity within it. If the ball is heated,the volume of the cavity will

The gap between any two rails, each of length $l$ laid on a railway track, is equal to $x$ at $27\,^{\circ}C$. When the temperature rises to $40\,^{\circ}C$, the gap closes up. If the coefficient of linear expansion of the material of the rail is $\alpha$, the length $l$ of a rail at $27\,^{\circ}C$ is:

$A$ $50 \ cm$ iron rod is connected to a $100 \ cm$ aluminum rod at $20^{\circ}C$. If $\alpha_{Fe} = 12 \times 10^{-6} {^{\circ}C}^{-1}$ and $\alpha_{Al} = 24 \times 10^{-6} {^{\circ}C}^{-1}$,what is the effective coefficient of linear expansion of the system?

$A$ brass disc fits snugly in a hole of a steel plate. The disc can be loosened from the hole if the system:

$A$ uniform metal bar of length $10 \ m$ with a crack at its midpoint is clamped between two rigid supports. The bar buckles upward due to a temperature rise of $40^{\circ} C$. If the coefficient of linear expansion of the metal is $2.5 \times 10^{-6} {}^{\circ} C^{-1}$,the maximum displacement of the midpoint of the bar is: (in $cm$)

Coefficient of linear expansion of brass and steel rods are $\alpha_1$ and $\alpha_2$. Lengths of brass and steel rods are $l_1$ and $l_2$ respectively. If $(l_2 - l_1)$ is maintained same at all temperatures,which one of the following relations holds good?