A body of weight W is floating in a liquid. Its apparent weight will be :
A
equal to W
B
less than W
C
greater than W
D
zero
Text Solution
AI Generated Solution
The correct Answer is:
To determine the apparent weight of a body floating in a liquid, we can follow these steps:
### Step-by-Step Solution:
1. **Identify the Forces Acting on the Body**:
- The body has a weight \( W \) acting downwards due to gravity.
- The body experiences an upward buoyant force (upthrust) \( F_B \) due to the liquid.
2. **Apply the Condition for Floating**:
- When a body is floating, the upward buoyant force is equal to the downward weight of the body. Therefore, we can write:
\[
F_B = W
\]
3. **Define Apparent Weight**:
- The apparent weight of the body is the weight that is perceived when the body is submerged in the fluid. It can be calculated as:
\[
\text{Apparent Weight} = \text{Weight} - \text{Buoyant Force}
\]
- Substituting the values we have:
\[
\text{Apparent Weight} = W - F_B
\]
4. **Substitute the Buoyant Force**:
- Since we established that \( F_B = W \), we can substitute this into the equation:
\[
\text{Apparent Weight} = W - W
\]
5. **Calculate the Apparent Weight**:
- Simplifying the equation gives:
\[
\text{Apparent Weight} = 0
\]
### Final Answer:
The apparent weight of the body floating in the liquid is **0**.
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