Let T represent the true weight of a body, B the force of buoyancy on the body when immersed in a liquid. A represents the apparent weight of the body and W be twice the weight of liquid displaced by te body. Then which of the following relation is correct?

Options

A. T = B - A
B. T - B = A
C. T = B + A - W
D. T - A = W - B

Answer

To solve the problem, we need to analyze the relationships between the true weight of the body (T), the buoyant force (B), the apparent weight (A), and the weight of the liquid displaced (W).

### Step-by-Step Solution:

1. **Understanding the Forces:**
- The true weight of the body (T) acts downwards.
- The buoyant force (B) acts upwards when the body is submerged in the liquid.
- The apparent weight (A) is the weight that an observer would measure when the body is submerged in the liquid.

2. **Relation between True Weight, Buoyant Force, and Apparent Weight:**
- The apparent weight (A) can be expressed as:
\[ A = T - B \]
This equation shows that the apparent weight is the true weight minus the buoyant force acting on the body.

3. **Weight of Liquid Displaced:**
- According to Archimedes' principle, the buoyant force (B) is equal to the weight of the liquid displaced by the body.
- We are given that W is twice the weight of the liquid displaced:
\[ W = 2 \times (\text{Weight of liquid displaced}) = 2B \]

4. **Analyzing the Options:**
- From the first relation we derived, we have:
\[ T - B = A \quad \text{(Option 2)} \]
- This is a valid relationship.

5. **Checking Other Options:**
- For Option 3:
\[ T = A + B \]
If we substitute \(W = 2B\) into this equation, we find inconsistencies, leading to \(W = 0\), which contradicts our initial condition.
- For Option 4:
\[ T - W = T - A = W - B \]
Substituting \(W = 2B\) leads to valid conclusions, confirming that this relationship holds true.

6. **Conclusion:**
- The correct relations derived from the problem are:
- Option 2: \(T - B = A\)
- Option 4: \(W = 2B\)

### Final Answer:
The correct relations are:
- Option 2: \(T - B = A\)
- Option 4: \(W = 2B\)