An automobile engine develops \[100~kW\] when rotating at a speed of \[1800\text{ }rev/min\]. What torque does it deliver?
a) $350Nm$
b) $440Nm$
c) $531Nm$
d) $628Nm$

Hint: In order to calculate the torque, we need to use a formula i.e.
$P=\tau \omega $or $\tau =\dfrac{P}{\omega }$
Where P is power generated by the body and $\omega $ is angular velocity of the body.
We will make use of the above formula to get the desired result.

Complete step-by-step answer:
The power delivered by the torque $\tau $ exerted on rotating body is given by,
$\tau =\dfrac{P}{\omega }$
Here, $P=100KW=100,000W$
$\omega =\left( \dfrac{1800}{60} \right)\times 2\pi $
$=60\pi rad/\sec $
$\tau =\dfrac{{{10}^{5}}}{60\times 3.14}=531 Nm$

Thus, the correct answer to this question is option (c).

Note: Rotational dynamics is the study of forces and motions about an axis of rotation. Formulas such as Kinematic Equations and Newton's laws can be expressed in rotating coordinate frames.In rotational motion, we know that the particles of the object, while moving follow a circular path. Every particle in the rigid body moves in a circular path along a plane that is perpendicular to the axis and has its center on the same axis.A spinning or revolving object has angular velocity. Whenever the magnitude or direction of this angular velocity changes, the object has angular acceleration.Dynamics for rotational motion is completely analogous to linear or translational dynamics. Dynamics is concerned with force and mass and their effects on motion. For rotational motion, we will find direct analogs to force and mass that behave just as we would expect from our earlier experiences. Fan moving in the house, table fan, hand blender's blades motion are all examples of rotational motion.