Question

An automobile engine develops 10kW when rotating at a speed of 1800 rev/min. What torque does it deliver?
A. 53.06 N-m
B. 440 N-m
C. 524 N-m
D. 628 N-m

Answer 1

Hint: Torque can be defined as the ratio of power and angular velocity, power is given. Find the angular velocity using the formula $2\pi f$, where f is the frequency. Substitute the values of angular velocity and power to calculate the value of torque delivered.

Complete step by step answer:
We are given that an automobile engine develops 10kW when rotating at a speed of 1800 rev/min.
We have to calculate the torque delivered by the engine.
Torque is the force acting on an object which can cause the object to rotate about an axis.
Torque is the ratio of the power developed by the engine and the angular velocity with which it rotates.
$Torque = \dfrac{{Power}}{{AngularVelocity}}$
As we can see, 10 kW of power and a frequency 1800 rev/min are given.
Angular velocity can be calculated using $2\pi f$
Here the frequency f is given per minute. Convert it into per second.
$
  f = 1800rev/\min \\
  1\min = 60\sec \\
  f = \dfrac{{1800}}{{60}}rev/\sec \\
\implies f = 30rev/\sec \\
  AngularVelocity = 2\pi \times f \\
  \pi = 3.14 \\
   = 2 \times 3.14 \times 30 \\
  AngularVelocity = 188.4rev/\sec \\
 $
Power is given in kilowatts, convert it into watts and substitute the values of angular velocity, power in the Torque formula.
$
  Torque = \dfrac{{Power}}{{AngularVelocity}} \\
  Power = 10kW = 10 \times {10^3}W \\
  AngularVelocity = 188.4rev/\sec \\
  Torque = \dfrac{{10 \times {{10}^3}}}{{188.4}} \\
 \therefore Torque = \dfrac{{{{10}^4}}}{{188.4}} = 53.06Nm \\
 $
Therefore, the torque delivered by the automobile engine which developed 10kW when rotating at a speed of 1800 rev/min is 53.06 N-m.

So, the correct answer is “Option A”.

Note:
The units of Torque are Newton-metres which can also be said as Joule. Joule is a unit for energy. But torque is not energy. So to avoid this confusion we use Newton-metres as the units of Torque instead of Joules as it is not energy. Torque is not energy because energy is a scalar quantity and Torque is a vector quantity.