A body of weight `w_(1)` when floats in water displaces an amount of water `w_(2)`. Then `w_(1)ltw_(2)`. In this statement true or false?

Explanation

To determine whether the statement "A body of weight \( w_1 \) when floats in water displaces an amount of water \( w_2 \). Then \( w_1 < w_2 \)" is true or false, we can analyze the situation step by step.

### Step 1: Understand the concept of buoyancy
When a body floats in a fluid, it displaces a volume of fluid equal to the weight of the body. This is explained by Archimedes' principle, which states that the buoyant force acting on a submerged object is equal to the weight of the fluid that the object displaces.

**Hint:** Remember that buoyancy is the upward force exerted by the fluid on the submerged or floating body.

### Step 2: Define the weights
Let:
- \( w_1 \) = weight of the body
- \( w_2 \) = weight of the water displaced by the body

### Step 3: Apply Archimedes' Principle
According to Archimedes' principle, when the body is floating, the buoyant force \( F_b \) acting on the body is equal to the weight of the fluid displaced, which is \( w_2 \). Therefore, we can write:
\[ F_b = w_2 \]

### Step 4: Relate buoyant force to the weight of the body
The buoyant force \( F_b \) is also equal to the weight of the body \( w_1 \) when it is floating. Thus, we have:
\[ w_1 = F_b \]

### Step 5: Combine the equations
From the above two steps, we can equate the two expressions for the buoyant force:
\[ w_1 = w_2 \]

### Step 6: Evaluate the statement
The statement claims that \( w_1 < w_2 \). However, from our analysis, we have found that \( w_1 = w_2 \). Therefore, the statement is false.

### Conclusion
The statement "A body of weight \( w_1 \) when floats in water displaces an amount of water \( w_2 \). Then \( w_1 < w_2 \)" is **false**.

---