Question

If an ideal engine needs to transmit a torque of 200 Nm to maintain a rotor at a uniform angular speed of 300 rads\(^{-1}\), then the power required for the engine is:

• A. 30 kW
• B. 60 kW
• C. 90 kW
• D. 150 kW
• E. 300 kW

Hint:

Power transmitted by a rotating body is the product of the torque and angular velocity. Ensure that the units of torque and angular velocity are consistent to calculate the power in watts or kilowatts.

Answer 1

The Correct Option is B

The power (\( P \)) transmitted by a torque is given by the formula: \[ P = \tau \omega \] where: - \( P \) is the power,
- \( \tau \) is the torque,
- \( \omega \) is the angular velocity.
Given: - Torque \( \tau = 200 \, {Nm} \),
- Angular velocity \( \omega = 300 \, {rads}^{-1} \).
Substituting these values into the formula for power: \[ P = 200 \times 300 = 60000 \, {W} = 60 \, {kW} \] Thus, the power required for the engine is: \[ \boxed{60 \, {kW}} \]