A hollow cylinder of radius R and length R is cut into four equal parts from its axis. Each one is called quarter cylinder. If the quarter cylinder is just completely immersed in a liquid of density ` rho `, find the horizontal thrust acting on the curved surface of the cylinder.

Options

A. ` rho g R^3 `
B. ` (1)/(2) rho g R^3 `
C. ` 2 rho g R ^3 `
D. ` (1)/(3) rho g R^ 3 `

Answer

B

Explanation

The horizontal thrust on the curved surface of the cylinder is
`F_n = rho _g Y_C A _ v `
where ` Y_C = (R )/(2) , A _ v = R^2 ` = vertical projection CDEF of the curved (cylindrical) surface ABCD.
This gives ` F_h = (1)/(2) rho g R ^ 3 `