A wooden block of mass m tied to a string is attached to bottom of a vessel containing water and it is fully immersed. If buoyant force = 2 mg then

1. Break Down the Problem

To understand the situation, we must identify the forces acting on the wooden block when it is fully immersed in water. The relevant forces include:

1. The weight of the wooden block (downward force).
2. The buoyant force acting on it (upward force).

2. Relevant Concepts

• Weight of the block: $W = mg$, where $m$ is the mass of the block and $g$ is the acceleration due to gravity.
• Buoyant force $F_b$: It is given that $F_b = 2mg$.

3. Analysis and Detail

Given that the buoyant force is twice the weight of the block, we can analyze the forces:

• Weight of the block: $W = mg$.
• Buoyant force: $F_b = 2mg$ (as provided).

4. Verify and Summarize

Since the buoyant force is greater than the weight of the block, it implies that the block will experience a net upward force. The net force acting on the block can be calculated as:

$F_{\text{net}} = F_b - W = 2mg - mg = mg$

This indicates that the block will accelerate upwards due to the net force $mg$.

Final Answer

The wooden block will accelerate upwards with an acceleration of $g$ because the net upward force is $mg$.