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 a) 10 kW b) 100 kW c)10 MW d) 100 MW

Options

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

Explanation

To find the power of the engine required to maintain a rotor at a uniform angular speed, we can use the relationship between power, 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:
\[ P = τ \cdot ω \]
where:
- P is the power in watts (W)
- τ is the torque in Newton meters (N·m)
- ω is the angular speed in radians per second (rad/s)

3. **Substitute the Values:**
Substitute the given values into the formula:
\[ P = 100 \, \text{N·m} \cdot 100 \, \text{rad/s} \]

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

5. **Convert to Kilowatts:**
Since the options are given in kilowatts (kW), convert watts to kilowatts:
\[ P = 10000 \, \text{W} = 10 \, \text{kW} \]

6. **Select the Correct Option:**
The answer is 10 kW, which corresponds to option (a).

### Final Answer:
The power of the engine is **10 kW** (option a).

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