Suppose the earth was covered by an oceam of uniform depth `h,(hltltR)` Let `sigma` be densityof ocean and `p` be mean density of earth. Let `Deltag` be the approxemate difference of value of net acceleration duet to gravity between the bottom of the ocean and top `(Deltag=g_("top")-g_("bottom"))`. Choose the correct option.

Options

A. `Delta g=(4)/(3)piGh[2p-3sigma]`
B. `Delta g=(4)/(3)Gpih[3sigma-2p]`
C. `Deltag=(4)/(3)Gpih[2sigma-3sigma]`
D. `Deltag=(4)/(3)Gpih[3p-3sigma]`

Explanation

`g_(A)=(4)/(3)GpiRp`
`g_(e)=(G[(4)/(3)pipR^(3)+[(4)/(3)pi(R+h)^(3)-(4)/(3)piR^(2)]sigma])/(R+h)^(2)`
`=(4)/(3)GpipR[1-(2h)/(R)](4)/(3)Gpi[(R+h)-(1-(2h)/(R))R]sigma`
`Deltag=g_(B)-9_(A)=(4)/(3)piGh[3sigma-2p]`