When a cylinder is heated,its length increases by $2\%$. What is the percentage increase in its surface area (in $\%$)?

The volume of a metal sphere increases by $0.24\%$ when its temperature is raised by $40^{\circ}C$. The coefficient of linear expansion of the metal is .......... $^{\circ}C^{-1}$.

$A$ clock pendulum made of invar has a period of $0.5 \, s$ at $20^{\circ} C$. If the clock is used in a climate where the temperature averages to $30^{\circ} C$, how much time does the clock lose in each oscillation? (For invar, $\alpha = 9 \times 10^{-7} /{ }^{\circ} C$, $g = \text{constant}$)

$A$ clock which keeps correct time at $20^{\circ} C$, is subjected to $40^{\circ} C$. If the coefficient of linear expansion of the pendulum is $12 \times 10^{-6} /{ }^{\circ} C$, how much time will it gain or lose per day?

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

Three rods of length $\ell$ each are joined to form an equilateral triangle $PQR$. $O$ is the midpoint of $PQ$. For a small change in temperature,the distance $OR$ remains constant. If the coefficient of linear expansion for $PR$ and $RQ$ is $\alpha_2$ and for $PQ$ is $\alpha_1$,then: