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 need to find the volume of water displaced by a body that experiences a loss of weight of 10 N when fully immersed in water. We can use the principle of buoyancy, which states that the buoyant force (upthrust) acting on a submerged object is equal to the weight of the fluid displaced by that object.

### Step-by-Step Solution:

1. **Understand the relationship between weight loss and buoyancy:**
- The loss of weight of the body when immersed in water is equal to the buoyant force acting on it.
- Mathematically, this can be expressed as:
\[ \text{Loss of weight} = \text{Buoyant force} = \text{Weight of displaced water} \]

2. **Express the weight of the displaced water:**
- The weight of the displaced water can be expressed using the formula:
\[ \text{Weight of displaced water} = \text{mass of displaced water} \times g \]
- The mass of the displaced water can be expressed in terms of its volume and density:
\[ \text{mass of displaced water} = \text{density of water} \times \text{volume of displaced water} \]
- Therefore, we can write:
\[ \text{Weight of displaced water} = \rho \times V \times g \]
where \( \rho \) is the density of water, \( V \) is the volume of displaced water, and \( g \) is the acceleration due to gravity.

3. **Set up the equation:**
- Since the loss of weight is given as 10 N, we can set up the equation:
\[ 10 \, \text{N} = \rho \times V \times g \]

4. **Substitute known values:**
- The density of water (\( \rho \)) is approximately \( 1000 \, \text{kg/m}^3 \) and the acceleration due to gravity (\( g \)) is approximately \( 10 \, \text{m/s}^2 \).
- Substituting these values into the equation gives:
\[ 10 = 1000 \times V \times 10 \]

5. **Solve for the volume \( V \):**
- Rearranging the equation to solve for \( V \):
\[ V = \frac{10}{1000 \times 10} = \frac{10}{10000} = 0.001 \, \text{m}^3 \]
- Converting this to cubic meters:
\[ V = 10^{-3} \, \text{m}^3 \]

6. **Conclusion:**
- The volume of water displaced by the body is \( 10^{-3} \, \text{m}^3 \).

### Final Answer:
The amount of water displaced by the body is \( 10^{-3} \, \text{m}^3 \).

---