Two cylindrical vessels of equal cross sectional area contain water up to heights ${\mathrm{h}}_1\left(>{\mathrm{h}}_2\right)$   and ${\mathrm{h}}_2$ . The vessels are inter connected so that the levels in them become equal. Calculate the work done by the force of gravity during this process if  $\mathrm{\rho }$ is the density of water.

• A

  $\mathrm{\rho A}{\left(\frac{{\mathrm{h}}_1-{\mathrm{h}}_2}{2}\right)}^2\mathrm{g}$

• B

  $\mathrm{\rho A}{\left(\frac{{\mathrm{h}}_1+{\mathrm{h}}_2}{2}\right)}^2\mathrm{g}$

• C

  $\frac{{\mathrm{\rho Ah}}_2^2\mathrm{g}}{{\mathrm{h}}_1}$

• D

  $\frac{{\mathrm{\rho Ah}}_1^2\mathrm{g}}{{\mathrm{h}}_2}$