A raft of wood (density $600 k g / m^{3}$ ) of mass $120 k g$ floats in water. The weight that can be put on the raft to make it just sink is :

120 k g

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200 k g

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40 k g

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80 k g

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Solution

The correct option is D $80 k g$
Density of raft = $600 k g / m^{3}$
mass of raft $= 120 k g$
Volume of wood $= \frac{120}{600} m^{3}$ $= \frac{1}{5} m^{3}$
So, Total upthrust from water if the raft is fully dipped in water $\frac{1}{5} \times 1000 k g / m^{3}$ $= 200$ kg
So, the raft will sink if total upthrust = total downward force,
So, weight that can be $(200 - 120) k g$ $= 80$ kg

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