Question

A raft of wood $(\rho =600{\text{kg/m}}^3)$ of mass $120\text{kg}$ floats on water. The mass which can be put on the raft to make it just sink is

• A. $20\text{kg}$
• B. $40\text{kg}$
• C. $100\text{kg}$
• D. $80\text{kg}$

Answer 1

The correct option is D $80\text{kg}$

Condition for a body to just sink is,
$\text{Weight of body}=\text{Buoyant force}$
Let the mass $m$ that can be put on the raft to make it just sink.
$\Rightarrow (M+m)g=F_b...\left(i\right)$
$\&F_b={\rho }_{l}gV$
where ${\rho }_l=1000{\text{kg/m}}^3$, is the density of liquid (water)
$V$ is volume of raft.
$V=\frac{\text{Mass of raft}}{\text{density of raft}}$
$\Rightarrow V=\frac{120}{600}$
Substituting in Eq.$\left(i\right)$,
$(120+m)\times 10=1000\times 10\times \frac{120}{600}$
$\therefore m=80\text{kg}$
Hence, $80\text{kg}$ of mass can be put on the raft to make it just sink.