A crane lifts a mass of 100 kg to a height of 10 m in 20 s. The power of the crane is (Take `g = 10 m s^(-2)`)

Options

A. 100 W
B. 200 W
C. 250 W
D. 500 W

Explanation

To find the power of the crane lifting a mass, we can follow these steps:

### Step 1: Identify the given values
- Mass (m) = 100 kg
- Height (h) = 10 m
- Time (t) = 20 s
- Acceleration due to gravity (g) = 10 m/s²

### Step 2: Calculate the potential energy (PE)
The potential energy (PE) gained by the mass when lifted to a height is given by the formula:
\[ PE = m \cdot g \cdot h \]

Substituting the values:
\[ PE = 100 \, \text{kg} \cdot 10 \, \text{m/s}^2 \cdot 10 \, \text{m} \]
\[ PE = 100 \cdot 10 \cdot 10 = 10000 \, \text{J} \]

### Step 3: Calculate the power (P)
Power is defined as the rate of doing work or the rate of energy transfer. It can be calculated using the formula:
\[ P = \frac{PE}{t} \]

Substituting the values:
\[ P = \frac{10000 \, \text{J}}{20 \, \text{s}} \]
\[ P = 500 \, \text{W} \]

### Conclusion
The power of the crane is 500 watts.

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