A metal rod of Young's modulus $Y$ and coefficient of thermal expansion $\alpha$ is held at its two ends such that its length remains invariant. If its temperature is raised by $t^{\circ} C$, the linear stress developed in it is

Water falls from a height $500m$. What is the rise in temperature of water at bottom if whole energy remains in the water ……….. $^\circ \mathrm{C}$

A glass flask is filled up to a mark with $50\, cc$ of mercury at $18°C.$ If the flask and contents are heated to $38°C.$ ……… $cc$ mercury will be above the mark $?$ $(\alpha$ for glass is $ 9 × 10^{-6}{°}C^{-1}$ and coefficient of real expansion of mercury is $180 × 10^{-6}{°}C^{-1})$ 

Show that the coefficient of area expansion, $(\Delta A / A) / \Delta T,$ of a rectangular sheet of the solid is twice its Iinear expansivity, $\alpha_{1}$

Coefficient of linear expansion of brass and steel rods are $\alpha_1$ and $\alpha_2$. Lengths of brass and steel rods are $l_1$ and $l_2$ respectively. If $\left(l_2-l_1\right)$ is maintained same at all temperatures, which one of the following relations holds good?