An iron rod has a length of $10 \ cm$ at $20^{\circ}C$. What will be the change in length of the iron rod at $19^{\circ}C$? (Given for iron,$\alpha = 11 \times 10^{-6} \ ^{\circ}C^{-1}$)

$A$ crystal has a linear expansion coefficient of $\alpha_1$ in one direction and $\alpha_2$ in all directions perpendicular to it. What will be the volume expansion coefficient of the crystal?

$A$ pendulum clock loses $12\;s$ a day if the temperature is $40^{\circ}C$ and gains $4\;s$ a day if the temperature is $20^{\circ}C$. The temperature at which the clock will show correct time,and the coefficient of linear expansion $(\alpha)$ of the metal of the pendulum shaft are respectively:

Two rods are joined between fixed supports as shown in the figure. The condition for no change in the total length of the system with an increase in temperature is given by:
($\alpha_1, \alpha_2$ = linear expansion coefficients,$A_1, A_2$ = cross-sectional areas of rods,$Y_1, Y_2$ = Young's moduli)

Obtain the relation between the coefficient of volume expansion $(\alpha_V)$ and the coefficient of linear expansion $(\alpha_l)$.

At what temperature (in $ ^{\circ} C$) should a gold ring of diameter $6.230 \,cm$ be heated so that it can be fitted on a wooden bangle of diameter $6.241 \,cm$ (in $.7$)? Both diameters were measured at room temperature $(27^{\circ} C)$. (Given: coefficient of linear thermal expansion of gold $\alpha_{L}=1.4 \times 10^{-5} \,K ^{-1}$)