According to Archimedes's principle the loss in of weight is equal to (V is the volume displaced by the body, `rho` is the density of liquid in which body is immersed)

Options

A. `Vrhog`
B. `2Vrhog`
C. `Vrhog/2`
D. `Vrhog/4`

Answer

To solve the question regarding Archimedes's principle and the loss of weight when a body is immersed in a fluid, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**:
- We need to find the loss in weight of a body when it is immersed in a liquid. According to Archimedes's principle, this loss in weight is equal to the weight of the liquid displaced by the body.

2. **Identify the Variables**:
- Let \( V \) be the volume of the liquid displaced by the body.
- Let \( \rho \) be the density of the liquid in which the body is immersed.
- The acceleration due to gravity is denoted as \( g \).

3. **Calculate the Weight of the Displaced Liquid**:
- The weight of the liquid displaced can be calculated using the formula:
\[ \text{Weight of displaced liquid} = \text{mass of displaced liquid} \times g \]
- The mass of the displaced liquid can be expressed as:
\[ \text{mass} = \text{density} \times \text{volume} = \rho \times V \]
- Therefore, the weight of the displaced liquid becomes:
\[ \text{Weight of displaced liquid} = \rho \times V \times g \]

4. **Relate True Weight and Apparent Weight**:
- The true weight \( W \) of the body is given by:
\[ W = m \times g \]
- The apparent weight \( W' \) of the body when submerged in the liquid is given by:
\[ W' = W - \text{Weight of displaced liquid} \]
- Substituting the weight of the displaced liquid into the equation gives:
\[ W' = W - \rho V g \]

5. **Determine the Loss in Weight**:
- The loss in weight when the body is immersed in the liquid is the difference between the true weight and the apparent weight:
\[ \text{Loss in weight} = W - W' = W - (W - \rho V g) = \rho V g \]

6. **Conclusion**:
- According to Archimedes's principle, the loss in weight of the body when immersed in the liquid is equal to:
\[ \text{Loss in weight} = \rho V g \]

### Final Answer:
The loss in weight is equal to \( \rho V g \).

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