Too maintain a rotor at a uniform angular speed of `100 rad s^(-1)`, an engine needs to transmit torque of 100 N m. The power of the engine is

Options

A. 10 kW
B. 100 kW
C. 10 MW
D. 100 MW

Explanation

To find the power of the engine required to maintain the rotor at a uniform angular speed, we can use the formula for power in terms of torque and angular speed.

### Step-by-step Solution:

1. **Identify the Given Values:**
- Angular speed (ω) = 100 rad/s
- Torque (τ) = 100 N·m

2. **Use the Power Formula:**
The power (P) transmitted by the engine can be calculated using the formula:
\[ P = τ \cdot ω \]

3. **Substitute the Given Values:**
Plugging in the values we have:
\[ P = 100 \, \text{N·m} \cdot 100 \, \text{rad/s} \]

4. **Calculate the Power:**
\[ P = 10000 \, \text{W} \]

5. **Convert to Kilowatts:**
Since 1 kW = 1000 W, we convert the power to kilowatts:
\[ P = \frac{10000 \, \text{W}}{1000} = 10 \, \text{kW} \]

### Final Answer:
The power of the engine is **10 kW**.

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