First slide

Fluid statics

Question

A boat 3 m long and 2 m wide is floating in a lake. When a man climbs over it, it sinks 1 cm further into water. The mass of the man is:

Moderate

A

60 kg
B

64 kg
C

70 kg
D

72 kg

Solution

Let mass of boat $= M_{b}$ and due to weight of boat, boat sink x_m then
$M_{b} g = (3 \times 2 \times x) ρ_{w} g (M_{b} + M_{m}) g = 3 \times 2 (x + 10^{- 2}) ρ_{w} g \Rightarrow M_{m} = (6 \times 10^{- 2}) \times ρ_{w} = 60 kg$

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