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

Options

A. 60 Kg
B. 72 kg
C. 12 kg
D. 128 kg

Explanation

To find the mass of the man who causes the boat to sink by 1 cm, we can follow these steps:

### Step 1: Calculate the volume of water displaced
The boat has a length of 3 m and a breadth of 2 m. When the man gets on the boat, it sinks by 1 cm (or 0.01 m).

The volume of water displaced (V) can be calculated using the formula:
\[ V = \text{length} \times \text{breadth} \times \text{depth} \]

Substituting the values:
\[ V = 3 \, \text{m} \times 2 \, \text{m} \times 0.01 \, \text{m} \]
\[ V = 0.06 \, \text{m}^3 \]

### Step 2: Calculate the mass of the water displaced
The mass of the water displaced (m) can be calculated using the formula:
\[ m = \text{density} \times \text{volume} \]

The density of water is approximately \( 1000 \, \text{kg/m}^3 \). Thus:
\[ m = 1000 \, \text{kg/m}^3 \times 0.06 \, \text{m}^3 \]
\[ m = 60 \, \text{kg} \]

### Conclusion
The mass of the man is \( 60 \, \text{kg} \).

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