A raft of wood of density 600 $kg{m}^{-3}$  and mass 120 kg floats in water. How much weight can be put on the raft to make it just sink?

detailed solution

Correct option is C

Volume of raft =120600=15m3 Fraction of volume inside water isρwoodρwater=Relative density = 6001000=35So, fraction of volume outside water is(1−35)=25⇒  volume outside water isVout=25×15=225m3When the body just sinks, the additional upthrust isU=225×103×gIf the weight put on the raft is m thenmg=225×103×10⇒  m=80 kgII method: fraction of raft=120600=15 Buoyant force=viρlg=15×1000 kgf=200kgf For floatation,  weight =upthrust 120+M=200 M=80kg