First slide

Fluid statics

Question

A raft of wood (density 600 kg/ $m^{3}$ ) of mass 150 kg floats in water. How much weight can be put on the raft to make it just sink?

Moderate

A

120 kg
B

200 kg
C

80 kg
D

100 kg

Solution

Volume of raft = V = $\frac{mass}{density}$
V = $\frac{150}{600} = \frac{1}{4} m^{3}$
When the raft is totally immersed in water, it displaces $\frac{1}{4} m^{3}$ water. so the upthrust.
= $\frac{1}{4} \times 1000 \times g newton$
If x kg is the extra weight put on the raft to fully immerse it in water, then
(x+150)g = $\frac{1}{4}$ x 1000 x g or = x+150 = 250
x = 100 kg

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