First slide

Fluid statics

Question

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

Moderate

A

80 kg
B

50 kg
C

60 kg
D

30 kg

Solution

Volume of log of wood V = $\frac{mass}{density} = \frac{120}{600}$
= 0.2 $m^{3}$
Let x be the weight that can be put on the log of wood.
So weight of the body = (120+x) $\times 10 N$
Weight of displaced liquid = $Vσg = 0.2 \times 10^{3} \times 10 N$
The body will just sink in liquid if the weight of the body will be equal to the weight of displaced liquid.
$∴ (120 + x) \times 110 = 0.2 \times 10^{3} \times 10$
$\Rightarrow 120 + x = 100 ∴ x = 80 kg$

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