Question

An automobile engine develops $100\text{hp}$ when rotating at a speed of $1800\text{rad/min}$. The torque delivered by the engine is:

• A. $5487\text{W-s}$
• B. $4487\text{W-s}$
• C. $3487\text{W-s}$
• D. $2487\text{W-s}$

Answer 1

The correct option is D $2487\text{W-s}$

Given:
Power, $P=100\text{hp}=74600\text{W}$
Angular speed, $\omega =1800\text{rad/min}=30\text{rad/s}$
Work done by torque is given by,
$dW=\tau d\theta$
$\Rightarrow \frac{dW}{dt}=\tau \frac{d\theta }{dt}$
$\Rightarrow P=\tau \omega$
$\Rightarrow \tau =\frac{P}{\omega }=\frac{74600}{30}\approx 2487\text{W-s}$

Why this question? Tips: $1\text{hp}=746\text{W}$ and $\text{N-m}$ as well as $\text{W-s}$ are unit of torque.