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 $40 \, ^oC$ in its temperature is:

The coefficient of volume expansion of glycerin is $5 \times 10^{-4} \ K^{-1}$. If the temperature of glycerin is raised by $40^{\circ} C$,the fractional change in its density will be . . . . . . .

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 coefficients of apparent expansion of a liquid when determined using two different vessels $A$ and $B$ are $\gamma_1$ and $\gamma_2$, respectively. If the coefficient of linear expansion of the vessel $A$ is $\alpha$, the coefficient of linear expansion of the vessel $B$ is

The coefficient of apparent expansion of a liquid when determined using two different vessels $A$ and $B$ are ${\gamma _1}$ and ${\gamma _2}$ respectively. If the coefficient of linear expansion of vessel $A$ is $\alpha $,the coefficient of linear expansion of vessel $B$ is

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