A body will weigh maximum in which case? Water or in vacuum

Answer

To determine in which case a body will weigh the maximum—whether in water or in a vacuum—we can analyze the forces acting on the body in both scenarios.

### Step-by-Step Solution:

1. **Understanding Weight**:
- The weight of a body is defined as the gravitational force acting on it, which is given by the formula:
\[ W = mg \]
where \( m \) is the mass of the body and \( g \) is the acceleration due to gravity.

2. **Weight in Vacuum**:
- When the body is in a vacuum, there are no other forces acting on it except for gravity. Therefore, the weight of the body in a vacuum is simply:
\[ W_{vacuum} = mg \]

3. **Weight in Water**:
- When the body is submerged in water, it experiences an additional force known as the buoyant force. The buoyant force (\( F_b \)) can be calculated using Archimedes' principle:
\[ F_b = \rho V g \]
where \( \rho \) is the density of the water, \( V \) is the volume of the displaced water, and \( g \) is the acceleration due to gravity.

4. **Net Weight in Water**:
- The apparent weight of the body when submerged in water is the actual weight minus the buoyant force:
\[ W_{water} = mg - F_b \]
Substituting the expression for buoyant force, we get:
\[ W_{water} = mg - \rho V g \]

5. **Comparison of Weights**:
- In the vacuum, the weight is \( mg \), while in water, the weight is reduced by the buoyant force:
\[ W_{water} = mg - \rho V g < mg \]
Therefore, the weight of the body in water is less than its weight in a vacuum.

6. **Conclusion**:
- From the above analysis, we conclude that the body will weigh maximum in a vacuum, as the weight in water is reduced due to the buoyant force acting on it.

### Final Answer:
A body will weigh maximum in a vacuum.