Rotational Power

Q. An automobile engine develops 100 kW when rotating at a speed of 1800 rev/min. What torque does it deliver

1. 350 N-m
2. 440 N-m
3. 531 N-m
4. 628 N-m

Q. The angular velocity of a body is $\overrightarrow{\omega }=2\hat{i}+3\hat{j}+4\hat{k}$ and a torque $\overrightarrow{\tau }=\hat{i}+2\hat{j}+3\hat{k}$ acts on it. The rotational power will be

1. 20 W
2. 15 W
3. $\sqrt{17}W$
4. $\sqrt{14}W$

Q. Due to application of a torque having a magnitude of 20 N-m, a ring is rotating at an angular velocity of 250 $\frac{rad}{s}$ at any given instant. What is the power delivered at this moment?

1. 2500 J/s
2. 5000 J/s
3. 1000 J/s
4. 1250 J/s