$A$ 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:

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 . . . . . . .

$A$ 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 $180 \times 10^{-6} {^{\circ}C}^{-1}$)

$A$ glass flask of volume $1 \, L$ is completely filled with mercury at $0 \, ^\circ C$. The temperature of the glass flask and mercury is raised to $100 \, ^\circ C$. If the coefficient of volume expansion of mercury is $1.82 \times 10^{-4} \, ^\circ C^{-1}$ and the coefficient of linear expansion of glass is $0.1 \times 10^{-4} \, ^\circ C^{-1}$,how much mercury will overflow from the flask? (in $cm^3$)

The apparent coefficient of expansion of a liquid when heated in a brass vessel is $X$ and when heated in a tin vessel is $Y$. If $\alpha$ is the coefficient of linear expansion for brass, the coefficient of linear expansion of tin is ..........

$A$ glass flask of volume $1 \text{ litre}$ is filled completely with mercury at $0^{\circ} C$. The flask is now heated to $100^{\circ} C$. The coefficient of volume expansion of mercury is $1.82 \times 10^{-4} /{ }^{\circ} C$ and the coefficient of linear expansion of glass is $0.1 \times 10^{-4} /{ }^{\circ} C$. During this process, the amount of mercury which overflows is (in $\text{ cc}$)