A motor boat having a length of 10m and breadth 5m is floating on a lake. The boat sinks by 5cm when load gets on it. What is the mass of load?

Options

A. 3000g
B. 2500kg
C. 4010kg
D. None

Explanation

To solve the problem, we need to determine the mass of the load that causes the boat to sink by 5 cm. We will use the principle of buoyancy, which states that the weight of the water displaced by the submerged part of the boat is equal to the weight of the load.

### Step-by-Step Solution:

1. **Identify the dimensions of the boat:**
- Length (L) = 10 m
- Breadth (B) = 5 m
- The boat sinks by a height (h) = 5 cm = 0.05 m

2. **Calculate the volume of water displaced:**
The volume (V) of water displaced when the boat sinks can be calculated using the formula:
\[ V = L \times B \times h \]
Substituting the known values:
\[ V = 10 \, \text{m} \times 5 \, \text{m} \times 0.05 \, \text{m} = 2.5 \, \text{m}^3 \]

3. **Determine the density of water:**
The density (\(\rho\)) of water is approximately:
\[ \rho = 1000 \, \text{kg/m}^3 \]

4. **Calculate the mass of the water displaced:**
The mass (m) of the water displaced can be calculated using the formula:
\[ m = \rho \times V \]
Substituting the values:
\[ m = 1000 \, \text{kg/m}^3 \times 2.5 \, \text{m}^3 = 2500 \, \text{kg} \]

5. **Conclusion:**
The mass of the load that causes the boat to sink by 5 cm is:
\[ \text{Mass of load} = 2500 \, \text{kg} \]

### Final Answer:
The mass of the load is **2500 kg**.