A boat floating in a lake sinks by 2 cm when a man of mass m gets into it. What will be the mass of man if length and breadth of the boat are 1 m and 2 m?

Options

A. 40 kg
B. 60 kg
C. 30 kg
D. 100 kg

Explanation

To solve the problem of how much mass the man has when he gets into the boat, we can follow these steps:

### Step 1: Understand the situation
The boat is floating in a lake and sinks by 2 cm when a man of mass \( m \) gets into it. We need to find the mass of the man.

### Step 2: Identify the dimensions of the boat
The dimensions of the boat are given as:
- Length \( L = 1 \, \text{m} \)
- Breadth \( B = 2 \, \text{m} \)

### Step 3: Calculate the volume of water displaced
When the boat sinks by 2 cm (which is \( 0.02 \, \text{m} \)), the volume of water displaced by the boat can be calculated using the formula for volume:
\[ \text{Volume displaced} = L \times B \times H \]
where \( H \) is the height the boat sinks, which is \( 0.02 \, \text{m} \).

Substituting the values:
\[ \text{Volume displaced} = 1 \, \text{m} \times 2 \, \text{m} \times 0.02 \, \text{m} = 0.04 \, \text{m}^3 \]

### Step 4: Calculate the mass of water displaced
The mass of the water displaced can be found using the formula:
\[ \text{Mass} = \text{Volume} \times \text{Density} \]
The density of water is approximately \( 1000 \, \text{kg/m}^3 \).

Thus,
\[ \text{Mass of water displaced} = 0.04 \, \text{m}^3 \times 1000 \, \text{kg/m}^3 = 40 \, \text{kg} \]

### Step 5: Relate the mass of the man to the mass of water displaced
According to Archimedes' principle, the weight of the water displaced is equal to the weight of the man. Therefore, the mass of the man \( m \) is equal to the mass of the water displaced:
\[ m = 40 \, \text{kg} \]

### Conclusion
The mass of the man is \( 40 \, \text{kg} \).

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