A Pitot tube is shown in figure. Wind blows in the direction shown. Air at inlet A is brought to rest, whereas its speed just outside of opening B is unchanged. The U tube contains mercury of density ${\mathrm{\rho }}_{\mathrm{m}}$. Find the speed of wind with respect to Pitot tube. Neglect the height difference between A and B and take the density of air as ${\mathrm{\rho }}_{\mathrm{a}}$.

• A

  $\sqrt{\frac{2({\mathrm{\rho }}_{\mathrm{m}}+{\mathrm{\rho }}_{\mathrm{a}})\mathrm{gh}}{{\mathrm{\rho }}_{\mathrm{a}}}}$

• B

  $\sqrt{\frac{2({\mathrm{\rho }}_{\mathrm{m}}-{\mathrm{\rho }}_{\mathrm{a}})\mathrm{gh}}{{\mathrm{\rho }}_{\mathrm{a}}}}$

• C

  $\sqrt{\frac{({\mathrm{\rho }}_{\mathrm{m}}-{\mathrm{\rho }}_{\mathrm{a}})\mathrm{gh}}{{\mathrm{\rho }}_{\mathrm{a}}}}$

• D

  $\sqrt{\frac{({\mathrm{\rho }}_{\mathrm{m}}+{\mathrm{\rho }}_{\mathrm{a}})\mathrm{gh}}{{\mathrm{\rho }}_{\mathrm{a}}}}$