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: Understand the formula for power
Power (P) is defined as the work done (W) per unit time (t). The formula is:
\[ P = \frac{W}{t} \]

### Step 2: Calculate the work done (W)
The work done in lifting an object is given by the formula:
\[ W = m \cdot g \cdot h \]
where:
- \(m\) = mass (in kg)
- \(g\) = acceleration due to gravity (in m/s²)
- \(h\) = height (in m)

Given:
- \(m = 100 \, \text{kg}\)
- \(g = 10 \, \text{m/s}^2\)
- \(h = 10 \, \text{m}\)

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

### Step 3: Calculate the power (P)
Now that we have the work done, we can calculate the power using the time taken (t = 20 s):
\[ P = \frac{W}{t} = \frac{10000 \, \text{J}}{20 \, \text{s}} = 500 \, \text{W} \]

### Final Answer
The power of the crane is:
\[ \boxed{500 \, \text{W}} \]