Brass and lead rods of length $80 \ cm$ are connected in parallel at $0^{\circ}C$. If they are heated to $100^{\circ}C$,what will be the difference in length between their ends in $mm$? (Given: $\alpha_{brass} = 18 \times 10^{-6} \ ^{\circ}C^{-1}$ and $\alpha_{lead} = 28 \times 10^{-6} \ ^{\circ}C^{-1}$)

$A$ rod of length $10 \, m$ at $0 \, ^oC$ has a linear expansion coefficient $\alpha = (2x^2 + 1) \times 10^{-6} \, ^oC^{-1}$,where $x$ is the distance from one end of the rod. The length of the rod at $10 \, ^oC$ is: (in $, m$)

$A$ brass disc fits snugly in a hole of a steel plate. To loosen the disc from the hole, the system should be:

$A$ hole of diameter $5 \ cm$ is drilled in a metal sheet at $30^{\circ} C$. The coefficient of linear expansion of the metal is $2 \times 10^{-5} K^{-1}$. The diameter of the hole when the temperature is raised to $230^{\circ} C$ is equal to: (in $cm$)

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:

$A$ metal ball initially at a pressure of $10^5 \ Pa$ is heated from $20^{\circ} C$ to $127^{\circ} C$ while keeping its volume constant. The coefficient of linear expansion of the metal is $10^{-5} \ {^{\circ} C}^{-1}$ and the bulk modulus of the metal is $2 \times 10^{11} \ N \ m^{-2}$. The final pressure inside the ball becomes: