Question

A flat slab of styrofoam, with a density of 32kg/m^3 , floats on a lake.
What minimum volume must the slab have so that a 33kg boy can sit on the slab without it sinking?

Answer 1

let the volume be V ;

submerged volume = V ;

volume of water displaced = V ;

buoyant force = ρw V g ; -----------------1

downward force = 33 *g + ρs * V * g ------------2

but since body is in equilbrium , so eqn 1 = eqn 2 ,

ρw V g = 33 g + ρs * V * g

ρw V = 33 + ρs * V

or V ( 1000 - 32 ) = 33 ;

or V = 0.034090 m^3 <------------ans