A man thinks about 4 arrangements as shown to raise two small bricks each having mass m. Which of the arrangement would take minimum time ?

Options

A.
B.
C.
D.

Answer

To determine which arrangement takes the minimum time to raise two small bricks, each with mass \( m \), we need to analyze the acceleration produced in each arrangement. The key principle here is that to minimize time, we need to maximize acceleration, which in turn requires maximizing the net force acting on the system.

### Step-by-Step Solution:

1. **Understanding the Problem**:
We have four different arrangements to lift two bricks, and we need to find out which one allows for the maximum acceleration, thus minimizing the time taken to lift them.

2. **Applying Newton's Second Law**:
According to Newton's second law, the acceleration \( a \) of an object is given by the formula:
\[ a = \frac{F_{\text{net}}}{m} \]
where \( F_{\text{net}} \) is the net force acting on the object and \( m \) is its mass.

3. **Analyzing Each Arrangement**:
- **Arrangement A**: The force \( F \) is applied directly to the system, resulting in a total force of \( 2F \) acting on the two bricks. Thus, the acceleration is:
\[ a_A = \frac{2F}{2m} = \frac{F}{m} \]

- **Arrangement B**: Here, a force is applied to a wheel, and due to friction, the effective tension \( T \) is less than \( F \). Therefore, the acceleration is:
\[ a_B < \frac{F}{m} \]

- **Arrangement C**: The force \( F \) is applied to the string, resulting in a tension \( T = F \). The acceleration for this arrangement is:
\[ a_C = \frac{F}{2m} \]
(since the force is distributed between two masses).

- **Arrangement D**: Similar to arrangement C, the force is divided, leading to a lower effective tension. Thus, the acceleration is:
\[ a_D < \frac{F}{2m} \]

4. **Comparing Accelerations**:
From our calculations:
- \( a_A = \frac{F}{m} \)
- \( a_B < \frac{F}{m} \)
- \( a_C = \frac{F}{2m} \)
- \( a_D < \frac{F}{2m} \)

It is clear that \( a_A \) is the largest acceleration.

5. **Conclusion**:
Since arrangement A provides the maximum acceleration, it will take the minimum time to raise the two bricks. Therefore, the correct answer is:
\[ \text{Arrangement A takes the minimum time.} \]