The value of the coefficient of volume expansion of glycerin is $5 \times 10^{-4} \ K^{-1}$. The fractional change in the density of glycerin for a rise of $40^{\circ}C$ in its temperature is:

The coefficient of apparent expansion of mercury in a glass vessel is $132 \times 10^{-6} /^{\circ}C$ and in a steel vessel is $114 \times 10^{-6} /^{\circ}C$. If $\alpha$ for steel is $12 \times 10^{-6} /^{\circ}C$,then that of glass is:

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:

$A$ vertical column $50 \ cm$ long at $50^{\circ}C$ balances another column of the same liquid $60 \ cm$ long at $100^{\circ}C$. The coefficient of absolute expansion of the liquid is:

Where is the coefficient of volume expansion $\alpha_V$ greater: in alcohol or mercury?

$A$ liquid having a coefficient of cubical expansion $\gamma$ is filled in a container having a coefficient of linear expansion $\alpha$. If the liquid overflows upon heating,which of the following relations is correct?