Coolie A takes 1 min to raise a box of mass m through a height of 2.0 m. Another coolie B takes 30 s for the same job. Which one has greater power?

Options

A. Coolie A
B. Coolie B
C. Both have the same power
D. Cannot say

Explanation

To determine which coolie has greater power, we can follow these steps:

### Step 1: Understand the Concept of Power
Power is defined as the rate at which work is done. The formula for power (P) is given by:
\[ P = \frac{\text{Work Done}}{\text{Time Taken}} \]

### Step 2: Calculate Work Done
In this scenario, both coolies are raising a box of mass \( m \) through a height of \( h = 2.0 \, \text{m} \). The work done (W) against gravity can be calculated using the formula:
\[ W = m \cdot g \cdot h \]
where \( g \) is the acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \)). However, since the work done is the same for both coolies, we can denote it as \( W \) without needing to calculate its exact value.

### Step 3: Determine Time Taken by Each Coolie
- Coolie A takes \( t_A = 1 \, \text{min} = 60 \, \text{s} \).
- Coolie B takes \( t_B = 30 \, \text{s} \).

### Step 4: Calculate Power for Each Coolie
Using the power formula for each coolie:
- For Coolie A:
\[ P_A = \frac{W}{t_A} = \frac{W}{60} \]
- For Coolie B:
\[ P_B = \frac{W}{t_B} = \frac{W}{30} \]

### Step 5: Compare the Powers
Since the work done \( W \) is the same for both coolies, we can compare their powers by looking at the time taken:
- Coolie A's power:
\[ P_A = \frac{W}{60} \]
- Coolie B's power:
\[ P_B = \frac{W}{30} \]

Since \( \frac{W}{30} > \frac{W}{60} \), it follows that:
\[ P_B > P_A \]

### Conclusion
Coolie B has greater power than Coolie A because he takes less time to do the same amount of work.

---