Question

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

• A. $120kg$
• B. $40kg$
• C. $80kg$
• D. $200kg$

Answer 1

The correct option is C $80kg$

Find the volume of raft.
We know that,
Volume of raft $=V=\frac{mass}{density}$

Given,
Density of raft $=600kg/m^3$

$M=120kg$

As we know,

$V=\frac{mass}{density}$

$V=\frac{120}{600}=\frac{1}{5}{m}^3$

Find the Upthrust on raft.
We know that $B=Vpg$

When the raft is totally immersed in water, it displaces $\frac{1}{5}{m}^3$ water, so the upthrust.

Upthrust on ball = weight of displaced water

$=Vpg$

$=\frac{1}{5}\times 1000\times g$ newton

Find the weight of raft.
If $xkg$ is the extra weight put on the raft to fully immerse it in water, then,

$(x+120)g=\frac{1}{5}\times 1000\times g$

$x+120=200$

$x=80kg$