Question

If the diameter of a shaft is subjected to torque alone is doubled, then the horse power can be increased to:

• A. 2P
• B. 4P
• C. 8P
• D. 16P

Hint:

Always remember the power relationship with the diameter in torque applications: doubling the diameter increases power capacity significantly due to the fourth power relationship.

Answer 1

The Correct Option is D

Calculating the change in horsepower due to change in diameter.
The power transmitted by a shaft due to torque is proportional to the torque and the angular velocity. Torque itself is proportional to the polar moment of inertia, which for a circular shaft is proportional to the fourth power of the diameter. Therefore, doubling the diameter increases the polar moment of inertia by \(2^4 = 16\) times, hence the horsepower increases to 16P.