$A$ glass vessel of volume $V_0$ is completely filled with a liquid and its temperature is raised by $\Delta T$. What volume of the liquid will flow over,if the coefficient of linear expansion of glass is $\alpha_g$ and the coefficient of volume expansion of the liquid is $\gamma_L$?

$A$ liquid having a coefficient of cubical expansion $\gamma$ is kept in a copper vessel having a coefficient of linear expansion $\alpha = \frac{\gamma}{3}$. If heat is supplied to the vessel,the original level of the liquid in the vessel will

The real coefficient of volume expansion of glycerine is $0.000597 \text{ /}^{\circ}\text{C}$ and the linear coefficient of expansion of glass is $0.000009 \text{ /}^{\circ}\text{C}$. The apparent volume coefficient of expansion of glycerine is:

$A$ glass flask of volume $1 \ L$ 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 $cc$)

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):

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: