A circular metallic ring of radius $R$ has a small gap of width $d$. The coefficient of thermal expansion of the metal is $\alpha$ in appropriate units. If we increase the temperature of the ring by an amount $\Delta T$, then width of the gap

The volume of a metal sphere increases by $0.24\%$ when its temperature is raised by $40°C$. The coefficient of linear expansion of the metal is ………. $°C$

What is areal expansion ? Give definition and unit of coefficient of areal expansion.

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

The volume of the bulb of a mercury thermometer at $0^o C$ is $V_0$and cross section of the capillary is $A_0$. The coefficient of linear expansion of glass is $a_g$ $per ^o C$ and the cubical expansion of mercury $\gamma_m$ $per ^o C$. If the mercury just fills the bulb at $0^o C$, what is the length of mercury column in capillary at $T^o C.$