A cup `ABC` is kept in a liquid of density `rho` as shown in the figure. Find the vertical thrust on the cup by the liquid present in region `2`, if the maximum volume of the liquid that can be kept in the cup is equal to `V`.

Answer

`Vrhog`

Explanation

Let us divide the cup into two parts `AB` and `BC`. Liquid pushes the curved surface `AB` upwards and `BC` downwards.

Vertical of the liquid on `AB` is `Fv_(1)=V_(1)rhog`
where `V_(1)=` volume of the portion `ABDE` above `AB` similarly, the vertical thrust of liquid on `BC` is `F_(v_(2))=V_(2)rhog` where `V_(2) =` volume of the potion `ABCDE` above `BC`.

Hence the net vertical force on the curved surface `ABC` of the cup is `Fv=Fv_(2)=Fv_(1)=V_(2)rhog-V_(1)rhog=(V_(2)-V_(1))rhog=Vrhog`
Where `V=` volume of liquid in the cup shown as shaded portion.