$A$ solid metallic cube having a total surface area of $24 \; m^{2}$ is uniformly heated. If its temperature is increased by $10 \; ^{\circ}C$,calculate the increase in volume of the cube. (Given: $\alpha = 5.0 \times 10^{-4} \; ^{\circ}C^{-1}$)

Two rods,one of aluminum and another of steel,have initial lengths $l_1$ and $l_2$ respectively. They are joined together to form a single rod of length $(l_1 + l_2)$. If the coefficients of linear expansion for aluminum and steel are $\alpha_a$ and $\alpha_s$ respectively,and the increase in length for both rods is the same when the temperature of both is increased by $t \ ^\circ C$,then $\frac{l_1}{l_1 + l_2} = \dots$

The difference in length between an iron rod and a copper rod is $10 \ cm$ at all temperatures. If ${\alpha _{Fe}} = 11 \times {10^{ - 6}} \, ^\circ C^{ - 1}$ and ${\alpha _{Cu}} = 17 \times {10^{ - 6}} \, ^\circ C^{ - 1}$,what are their lengths respectively?

$A$ hole is drilled in a copper sheet. The diameter of the hole is $4.24 \; cm$ at $27.0 \; ^{\circ}C$. What is the change in the diameter of the hole when the sheet is heated to $227 \; ^{\circ}C$? (Coefficient of linear expansion of copper $\alpha = 1.70 \times 10^{-5} \; K^{-1}$)

The area of cross-section of a railway track is $0.01\, m^2$. The temperature variation is $10^{\circ}C$. The coefficient of linear expansion of the material of the track is $10^{-5} /^{\circ}C$. The energy stored per meter in the track is ...... $J/m$. (Young's modulus of the material of the track is $10^{11}\, Nm^{-2}$)

Two rods,one of aluminium and the other of steel,having initial lengths $L_1$ and $L_2$ are connected together to form a single rod of length $(L_1+L_2)$. The coefficients of linear expansion of aluminium and steel are $\alpha_1$ and $\alpha_2$ respectively. If the length of each rod increases by the same amount,when their temperatures are raised by $t^{\circ}C$,then the ratio $\frac{L_1}{L_1+L_2}$ will be