A liquid having coefficient of cubical expansion $\gamma $ is filled in the container having coefficient of linear expansion $\alpha $. If on heating the liquid overflows, then which of the following relations is correct?

$540\  g$ of ice at $0\ ^oC$ is mixed with $540\  g$ water at $80\  ^oC$. The final temperature of the mixture is

A pendulum clock keeps correct time at $0\ ^oC$. The thermal coefficient of linear expansion of the  material of the pendulum is $\alpha$. If the temperature rises to $t\ ^oC$, then the clock loses per day by (in second)

The rods of length $L_1$ and $L_2$ are made of materials whose coefficients of linear expansion are $\alpha _1$ and $\alpha _2$ respectively. If the difference between the two length is independent of temperatures, then

Mercury is of ten used in clinical thermometers. Which one of the following properties of mercury is not a reason for this?

The volume of a metal sphere increases by $0.15\%$ when its temperature is raised by $24\,^oC$.The coefficient of linear expansion of metal is