A solid cone of height H and base radius `H/2` floats in a liquid of density `rho`. It is hanging from the ceiling with the help of a string. The force by the fluid on the curved surface of the cone is (`P_(0) =` atmospheric pressure)

Options

A. `piH^(2)((P_(0))/4+(rhogH)/3)`
B. `piH^(2)((P_(0))/4+(rhogH)/6)`
C. `(piH^(2))/4((P_(0))/4+rhogH)`
D. `(piH^(2))/4(P_(0)+rhogH)`

Answer

B

Explanation

`1/3pi(H/2)^(2)Hrhog=(P_(0)+rhogH)pi(H/2)^(2)-Fv`
`F_(v)=P_(0)pi(H^(2))/4+rhog(H^(3))/4pi-(piH^(3)rhog)/12`
`=P_(0)(piH^(2))/4+(rhogH^(3)pi)/6`