The loss of weight of body is 10 N when body is completely immersed in water, then the amount of water displaced by that body is

Options

A. 10 `m^3`
B. `10 ^(-3) m^3`
C. 100 `m^3`
D. `10 ^(-2) m^3`

Answer

To solve the problem, we will use Archimedes' principle, which states that the buoyant force acting on a submerged object is equal to the weight of the fluid displaced by that object.

### Step-by-Step Solution:

1. **Understanding the Given Information**:
- The loss of weight of the body when fully immersed in water is given as 10 N. This loss of weight is equal to the buoyant force acting on the body.

2. **Applying Archimedes' Principle**:
- According to Archimedes' principle, the buoyant force (B) is equal to the weight of the water displaced by the body. Therefore, we can write:
\[ B = \text{Weight of water displaced} = 10 \, \text{N} \]

3. **Relating Weight to Volume**:
- The weight of the water displaced can be expressed in terms of its volume (V) and density (ρ):
\[ \text{Weight of water displaced} = \text{mass of water} \times g = \rho \times V \times g \]
- Here, \( \rho \) is the density of water (approximately \( 1000 \, \text{kg/m}^3 \)), and \( g \) is the acceleration due to gravity (approximately \( 10 \, \text{m/s}^2 \)).

4. **Setting Up the Equation**:
- We can set the equations equal to each other:
\[ 10 \, \text{N} = \rho \times V \times g \]
- Substituting the values for \( \rho \) and \( g \):
\[ 10 \, \text{N} = 1000 \, \text{kg/m}^3 \times V \times 10 \, \text{m/s}^2 \]

5. **Simplifying the Equation**:
- This simplifies to:
\[ 10 = 10000 \times V \]

6. **Solving for Volume**:
- To find the volume \( V \):
\[ V = \frac{10}{10000} = 0.001 \, \text{m}^3 \]

7. **Final Answer**:
- Therefore, the amount of water displaced by the body is:
\[ V = 0.001 \, \text{m}^3 \text{ or } 10^{-3} \, \text{m}^3 \]

### Summary:
The amount of water displaced by the body is \( 0.001 \, \text{m}^3 \).

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