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 . . . . . . .

Two vertical glass tubes filled with a liquid are connected by a capillary tube as shown in the figure. The tube on the left is put in an ice bath at $0^{\circ}C$ while the tube on the right is kept at $30^{\circ}C$ in a water bath. The difference in the levels of the liquid in the two tubes is $4 \, cm$ while the height of the liquid column at $0^{\circ}C$ is $120 \, cm$. The coefficient of volume expansion of the liquid is (Ignore expansion of the glass tube):

$A$ glass flask is filled up to a mark with $50\, cc$ of mercury at $18^{\circ}C.$ If the flask and contents are heated to $38^{\circ}C,$ how much mercury will be above the mark? (Given: $\alpha$ for glass is $9 \times 10^{-6} {^{\circ}C}^{-1}$ and the coefficient of real expansion of mercury is $180 \times 10^{-6} {^{\circ}C}^{-1}$)

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 change in density of mercury,when it is heated from $10^{\circ} C$ to $60^{\circ} C$ is (The coefficient of volume expansion of mercury is $18.2 \times 10^{-5} \ K^{-1}$) (in $\%$)

The densities of a liquid at $0^{\circ} C$ and $100^{\circ} C$ are respectively $1.0127 \ g/cm^3$ and $1 \ g/cm^3$. $A$ specific gravity bottle is filled with $300 \ g$ of the liquid at $0^{\circ} C$ up to the brim and it is heated to $100^{\circ} C$. Then, the mass of the liquid expelled in grams is: (Coefficient of linear expansion of glass $= 9 \times 10^{-6} /^{\circ} C$)