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

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:

Why is the coefficient of volume expansion zero for water at $4\,^{\circ}C$?

$A$ glass flask of volume $1 \, L$ at $0 \, ^oC$ is filled level full with mercury at this temperature. The flask and mercury are now heated to $100 \, ^oC$. How much mercury will spill out,if the coefficient of volume expansion of mercury is $1.82 \times 10^{-4} / ^oC$ and the coefficient of linear expansion of glass is $0.1 \times 10^{-4} / ^oC$? ............ $cc$

In a vertical $U-$tube containing a liquid,the two arms are maintained at different temperatures ${t_1}$ and ${t_2}$. The liquid columns in the two arms have heights ${l_1}$ and ${l_2}$ respectively. The coefficient of volume expansion of the liquid is equal to

The coefficient of linear expansion of a vessel completely filled with $Hg$ is $1 \times 10^{-5} /^{\circ} C$. If there is no overflow of $Hg$ on heating the vessel,then the coefficient of cubical expansion of $Hg$ is: