An engine develops 10 kW of power. How much time will it take to lift a mass of 200 kg to a height of 40 m (`g=10(m)/(sec^2)`)`?

Options

A. 4 sec
B. 5 sec
C. 8 sec
D. 10 sec

Explanation

To solve the problem of how much time it will take for an engine that develops 10 kW of power to lift a mass of 200 kg to a height of 40 m, we can follow these steps:

### Step 1: Calculate the Work Done
The work done (or energy required) to lift an object is given by the formula:
\[ \text{Work Done} = mgh \]
where:
- \( m \) = mass (200 kg)
- \( g \) = acceleration due to gravity (10 m/s²)
- \( h \) = height (40 m)

Substituting the values:
\[ \text{Work Done} = 200 \, \text{kg} \times 10 \, \text{m/s}^2 \times 40 \, \text{m} \]
\[ \text{Work Done} = 200 \times 10 \times 40 \]
\[ \text{Work Done} = 80000 \, \text{J} \]

### Step 2: Convert Power to SI Units
The power of the engine is given as 10 kW. We need to convert this into watts (SI unit):
\[ 10 \, \text{kW} = 10 \times 1000 \, \text{W} = 10000 \, \text{W} \]

### Step 3: Use the Power Formula to Find Time
Power is defined as the rate of doing work:
\[ \text{Power} = \frac{\text{Work Done}}{\text{Time}} \]
Rearranging this formula to find time:
\[ \text{Time} = \frac{\text{Work Done}}{\text{Power}} \]

Substituting the values we calculated:
\[ \text{Time} = \frac{80000 \, \text{J}}{10000 \, \text{W}} \]
\[ \text{Time} = 8 \, \text{s} \]

### Final Answer
The time taken to lift the mass of 200 kg to a height of 40 m is **8 seconds**.

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