A thin rod having a length of $1\; m$ and area of cross-section $3 \times 10^{-6}\,m ^2$ is suspended vertically from one end. The rod is cooled from $210^{\circ}\,C$ to $160^{\circ}\,C$. After cooling, a mass $M$ is attached at the lower end of the rod such that the length of rod again becomes $1\,m$. Young's modulus and coefficient of linear expansion of the rod are $2 \times 10^{11} Nm ^{-2}$ and $2 \times 10^{-5} K ^{-1}$, respectively. The value of $M$ is $…….kg .\left(\right.$ Take $\left.g=10\,m s ^{-2}\right)$

The apparent coefficient of expansion of a liquid when heated in a copper vessel is $C$ and when heated in a silver vessel is $S$. If $A$ is the linear coefficient of expansion of copper, then the linear coefficient of expansion of silver is

The volume of the bulb of a mercury thermometer at $0^o C$ is $V_0$and cross section of the capillary is $A_0$. The coefficient of linear expansion of glass is $a_g$ $per ^o C$ and the cubical expansion of mercury $\gamma_m$ $per ^o C$. If the mercury just fills the bulb at $0^o C$, what is the length of mercury column in capillary at $T^o C.$

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

A liquid with coefficient of volume expansion $\gamma$ is filled in a container of a material having the coefficient of linear expansion $\alpha$. If the liquid overflows on heating, then