1.

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 isA. `(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» Correct Answer - D
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`


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