A solid ball is completely immersed in a liquid. The coefficients of volume expansion of the ball and liquid are $3 × 10^{-6}$ and $8 × 10^{-6} per ^o C$ respectively. The percentage change in upthrust when the temperature is increased by $100 ^o C$ is ....... $\%$

The coefficient of linear expansion of crystal in one direction is ${\alpha _1}$ and that in every direction perpendicular to it is ${\alpha _2}$. The coefficient of cubical expansion is

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

The ratio of the coefficient of volume expansion of a glass container to that of a viscous liquid kept inside the container is $1 : 4$. What fraction of the inner volume of the container should the liquid occupy so that the volume of the remaining vacant space will be same at all temperatures ?

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?

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