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

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Solution

Calculate volume of wood.
Given,
Mass of wood $= 120 k g$

Let the volume of wood be $V$ .
Therefore,
Weight $= p_{w o o d} V g$

$120 g = 600 V g$

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

Calculate mass required.
Let the mass be added is $m$ , therefore

Total weight = buoyancy

$p_{w o o d} V g + m g = p_{w} V g$

$600 V g + m g = 1000 V g$

$m = 400 \times \frac{1}{5}$

$m = 80 k g$

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