Question

A cubical block of wood of edge a and density `rho` floats in water of density `2rho`. The lower surface of the cube just touches the free end of a mass less spring of force constant K fixed at the bottom of the vessel. The weight W put over the block so that it is completely immersed in water without wetting the weight is
A. `a(a^(2)rhog+k)`
B. `a(arhog+2k)`
C. `a((arhog)/(2)+2k)`
D. `a(a^(2)rhog+(k)/(2))`

Answer 1

Since density of block `=(1)/(2)` (density of water) `50%` of its volume is immersed in water in the second case, half of the volume of the block is futher immersed in water `W=` Extra up thrust `+` spring force
`=axxaxx(a)/(2)xx2rhoxxg+k(a)/(2)=a(a^(2)rhog+(k)/(2))`