A prism shaped styrofoam of density `rho_(styrofoam) (ltrho_(water))` is held completely submerged in water. It lies with its base horizontal. The base of foam is at depth `h_(0)` below water surface and atmospheric pressure is `P_(0)` Surface of water is open to atmosphere. Styrofoam prism is held in equilibrium by the string attached symmetrically as shown (Take `rho_(styrofoam)=rho_(f), rho_(water)=rho_(w))`.
Magnitude of force on any one of the slant face of styrofoam is

Options

A. `(P_(0)+rho_(w)g(h_(0)-sqrt(2)l))Ll`
B. `(P_(0)+rho_(w)g(h_(0)-l/sqrt(2))Ll`
C. `(P_(0)-rho_(w)g(h_(0)-l/sqrt(2)))Ll`
D. `(P_(0)+rho_(w)g(h_(0)-l/(2sqrt(2))))Ll`

Answer

D

Explanation

Average pressure on slant surface
`P_(avg)=((P_(0)+rho_(w)gh_(0))+(P_(0)+rho_(w)gh_(0)-1/sqrt(2)))/2=(P_(0)+rho_(w)gh_(0)-l/(2sqrt(2)))`
Force on any one of the slant face
`=(P_(0)+rho_(w)g(h_(0)-l/(2sqrt(2)))Ll`