The coefficient of linear expansion of glass is ${\mathrm{\alpha }}_{\mathrm{g}}{/}^{\circ }\mathrm{C}$ and cubical expansion of mercury is ${\mathrm{\gamma }}_{\mathrm{m}}{/}^{\circ }\mathrm{C}$. The volume of the bulb of mercury thermometer at 0°C is V₀ and cross section of the capillary is A_o. What is the length of mercury column in capillary at ${\mathrm{T}}^{\circ }\mathrm{C},$ if the mercury just fills the bulb at O°C ?

• A

  $\frac{{\mathrm{V}}_0\mathrm{T}\left({\mathrm{\gamma }}_{\mathrm{m}}+3{\mathrm{\alpha }}_{\mathrm{g}}\right)}{{\mathrm{A}}_0\left(1+2{\mathrm{\alpha }}_{\mathrm{g}}\mathrm{T}\right)}$

• B

  $\frac{{\mathrm{V}}_0\mathrm{T}\left({\mathrm{\gamma }}_{\mathrm{m}}-3{\mathrm{\alpha }}_{\mathrm{g}}\right)}{{\mathrm{A}}_0\left(1+2{\mathrm{\alpha }}_{\mathrm{g}}\mathrm{T}\right)}$

• C

  $\frac{{\mathrm{V}}_0\mathrm{T}\left({\mathrm{\gamma }}_{\mathrm{m}}+2{\mathrm{\alpha }}_{\mathrm{g}}\right)}{{\mathrm{A}}_0\left(1+3{\mathrm{\alpha }}_{\mathrm{g}}\mathrm{T}\right)}$

• D

  $\frac{{\mathrm{V}}_0\mathrm{T}\left({\mathrm{\gamma }}_{\mathrm{m}}-2{\mathrm{\alpha }}_{\mathrm{g}}\right)}{{\mathrm{A}}_0\left(1+3{\mathrm{\alpha }}_{\mathrm{g}}\mathrm{T}\right)}$