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 solve the problem of determining which arrangement will take the minimum time to raise two small bricks each having mass \( m \), we need to analyze the forces acting on each arrangement and how they affect the acceleration of the bricks.

### Step-by-Step Solution:

1. **Understanding the Arrangements**:
We have four arrangements (A, B, C, D) for raising the two bricks. Each arrangement will have a different configuration affecting the forces acting on the bricks.

2. **Force Analysis**:
- In each arrangement, a force \( F \) is applied to lift the bricks.
- The total force acting on the bricks will determine the acceleration according to Newton's second law, \( F = ma \).

3. **Calculating Effective Force**:
- For arrangement A, if both bricks are lifted directly, the effective force is \( 2F \) (since both bricks are being lifted together).
- For arrangement B, if the force is distributed, we need to analyze how much force is effectively lifting the bricks.
- For arrangement C, if there are pulleys or friction involved, we need to consider how these factors reduce the effective force.

4. **Acceleration Calculation**:
- The acceleration \( a \) of the bricks can be calculated using \( a = \frac{F_{\text{effective}}}{2m} \).
- The arrangement with the highest effective force will have the highest acceleration.

5. **Time Calculation**:
- The time taken to lift the bricks can be derived from the kinematic equation \( s = ut + \frac{1}{2}at^2 \). Assuming the initial velocity \( u = 0 \), we can simplify this to \( s = \frac{1}{2}at^2 \).
- Rearranging gives \( t = \sqrt{\frac{2s}{a}} \). Therefore, the arrangement with the highest acceleration will take the least time.

6. **Conclusion**:
- After analyzing the forces and accelerations in each arrangement, we find that arrangement A, which applies the force directly to both bricks, results in the highest effective force and thus the highest acceleration.
- Therefore, **Arrangement A** will take the minimum time to raise the two bricks.