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 $T^o C.$
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 $T^o C.$
- A
$\frac{{{V_0}T\left( {{\gamma _m}\, - \,3{a_g}} \right)}}{{{A_0}\left( {1\, + \,2{a_g}T} \right)}}$
- B
$\frac{{{V_0}T\left( {{\gamma _m}\, - \,3{a_g}} \right)}}{{{A_0}\left( {1\, + \,2{a_g}T} \right)}}$
- C
$\frac{{{V_0}T\left( {{\gamma _m}\, + \,2{a_g}} \right)}}{{{A_0}\left( {1\, + \,3{a_g}T} \right)}}$
- D
$\frac{{{V_0}T\left( {{\gamma _m}\, + \,2{a_g}} \right)}}{{{A_0}\left( {1\, + \,3{a_g}T} \right)}}$
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- [JEE MAIN 2021]