A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of the man is:

Problem Restatement

Determine the man's mass from the additional volume of water displaced when the boat sinks by 1 cm.

Given data

• Boat plan dimensions: length = 3 m, breadth = 2 m (area = 6 m^2)
• Sinking (extra draft) = 1 cm = 0.01 m
• Density of water = 1000 kg/m^3

Concept / Approach

By Archimedes' principle, additional weight supported = weight of extra water displaced. Mass = density × displaced volume.

Step-by-step calculation

Extra displaced volume = Area × Extra draft = 6 × 0.01 = 0.06 m^3Mass of displaced water = 1000 × 0.06 = 60 kg

Final Answer

Mass of the man = 60 kg.