A body is just floating on the surface of a liquid. The density of the body is the same as that of the liquid. The body is slightly pushed down. What will happen to the body?

Options

A. come back slowly to its earlier position
B. remain submerged where it is left
C. sink in liquid
D. come out vigoursly

Explanation

To solve the problem, we will analyze the situation step by step.

### Step 1: Understand the Initial Condition
The body is floating on the surface of a liquid, and the density of the body (ρ_s) is equal to the density of the liquid (ρ_l). This means that the weight of the body is balanced by the buoyant force acting on it.

**Hint:** Recall that for an object to float, the buoyant force must equal the weight of the object.

### Step 2: Analyze the Forces Acting on the Body
In the floating condition, the forces acting on the body are:
- The weight of the body (W = m * g), acting downward.
- The buoyant force (F_b), acting upward, which is equal to the weight of the liquid displaced by the submerged part of the body.

Since the body is floating, we have:
\[ W = F_b \]
This implies that the volume of the liquid displaced is equal to the volume of the body submerged.

**Hint:** Use the principle of buoyancy which states that the buoyant force is equal to the weight of the fluid displaced.

### Step 3: Consider the Effect of Pushing the Body Down
When the body is slightly pushed down, it displaces more liquid. However, since the density of the body is equal to that of the liquid, the buoyant force will adjust to equal the weight of the body again.

**Hint:** Think about what happens to the buoyant force when the volume of the submerged part of the body increases.

### Step 4: Analyze the Resulting Motion
When the body is pushed down, the buoyant force temporarily decreases because the body is not fully submerged. However, as soon as the pushing force is removed, the buoyant force will become equal to the weight of the body again, causing the body to rise back to its original floating position.

**Hint:** Consider the restoring force that acts when the body is displaced from its equilibrium position.

### Step 5: Conclusion
Since the buoyant force will always adjust to equal the weight of the body when it is floating, the body will return to its original position after being pushed down. Therefore, the correct answer is:

**Option A:** The body will come back slowly to its earlier position.

### Final Answer
The body will come back slowly to its earlier position after being pushed down.

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