The volume of the bulb of a mercury thermometer at $0^\circ C$ is $V_0$ and the cross-section of the capillary is $A_0$. The coefficient of linear expansion of glass is $a_g$ per $^\circ C$ and the coefficient of cubical expansion of mercury is $\gamma_m$ per $^\circ C$. If the mercury just fills the bulb at $0^\circ C$,what is the length of the mercury column in the capillary at $T^\circ C$?
- A$\frac{V_0 T (\gamma_m - 3a_g)}{A_0 (1 + 2a_g T)}$
- B$\frac{V_0 T (\gamma_m - 3a_g)}{A_0 (1 + 3a_g T)}$
- C$\frac{V_0 T (\gamma_m + 2a_g)}{A_0 (1 + 3a_g T)}$
- D$\frac{V_0 T (\gamma_m + 3a_g)}{A_0 (1 + 2a_g T)}$
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