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. `pi H ^ 2 ((P_0)/(4 ) + (rho gH )/(3)) `
B. ` pi H^ 2 ((P_0)/(4) + (rho gH)/(6)) `
C. `(pi H^ 2 )/(4 ) ((P_0)/(4) + rho gH ) `
D. `(pi H^ 2 )/(4 ) (P_0 + rho gH ) `

Answer

B

Explanation

`(1)/(3)pi((H)/(2))^(2)Hpg=(P_(0)+pgH)pi((H)/(2))^(2)-F_(c)`
Where `F_(c)` = force by fluid on curved surface of cone. `Rightarrow F_(c)=P_(0)(piH^(2))/(4)+(rhogH^(3)pi)/(6)`