The volume of a metal sphere increases by $0.15\%$ when its temperature is raised by $24\,^{\circ}C$. The coefficient of linear expansion of the metal is:

$A$ cylinder has a piston at a temperature of $30^{\circ} C$. There is an all-round clearance of $0.08 \ mm$ between the piston and the cylinder wall. If the internal diameter of the cylinder is $15 \ cm$,what is the temperature at which the piston will fit into the cylinder exactly (in $^{\circ} C$)? $(\alpha_p = 1.6 \times 10^{-5} /^{\circ} C$ and $\alpha_c = 1.2 \times 10^{-5} /^{\circ} C)$

$A$ bimetallic strip is formed out of two identical strips, one of copper and the other of brass. The coefficients of linear expansion of the two metals are $\alpha_C$ and $\alpha_B$. On heating, the temperature of the strip increases by $\Delta T$ and the strip bends to form an arc of radius $R$. Then $R$ is proportional to

The length of a metal rod at $30^{\circ} C$ is $30 \ cm$. If its temperature is raised to $105^{\circ} C$, its length is increased by $0.027 \ cm$. Then the coefficient of linear expansion of the metal is

$A$ simple pendulum made of a bob of mass $m$ and a metallic wire of negligible mass has a time period $2 \ s$ at $T = 0 \ ^oC$. If the temperature of the wire is increased and the corresponding change in its time period is plotted against its temperature,the resulting graph is a line of slope $S$. If the coefficient of linear expansion of the metal is $\alpha$,then the value of $S$ is:

$A$ rod of length $2 \ m$ rests on a smooth horizontal floor. If the rod is heated from $0^\circ C$ to $20^\circ C$, find the longitudinal thermal strain developed? $(\alpha = 5 \times 10^{-5} / ^\circ C)$