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A hemispherical portion of radius R is r...

A hemispherical portion of radius R is removed from the bottom of a cylinder of radius R. The volume of the remaining cylinder is V and its mass M. It is suspended by a string in a liquid of density `rho` where it stays vertical. The upper surface of the cylinder is at a depth h below the liquid surface. The force on the bottom of the cylinder by the liquid is

A

(a) `Mg`

B

(b) `Mg-Vrhog`

C

(c) `Mg+piR^2hrhog`

D

(d) `rhog(V+piR^2h)`

Text Solution

Verified by Experts

The correct Answer is:
D
KEY CONCEPT:
According to Archimendes principle
Upthrust=Wt.of fluid displaced
`F_(b ot t om)-F_(t op)=Vrhog`
`:. F_(b ot t om)=F_(t op)+Vrhog`
`=P_1xxA+Vrhog`
`=(hrhog)xx(piR^2)+Vrhog`
`=rhog[piR^2h+V]`
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