Question

A diesel engine develops a power of \[90W\] at $ \dfrac{600}{\pi } $ rpm. The torque it can exert at the given angular speed is (in N-m)
A. $ 4.5 $
B. $ 45 $
C. $ 0.45 $
D. $ 9\pi $

Answer 1

Hint: Diesel engine can be defined as any internal-combustion engine in which air is compressed to a sufficiently high temperature to ignite diesel fuel injected into the cylinder inside it, where combustion and expansion activate a piston. It converts the chemical energy stored in the fuel into mechanical energy, and thus is used to power freight trucks, large tractors, and other heavy locomotives.
And, Torque is the measure of the force that can cause an object to rotate about an axis which can be formulated as \[Torque=\dfrac{Power}{Angular\text{ }velocity}\]in terms of power and angular velocity.

Complete step-by-step answer:
From the given question, we can acquire the following information:
The power generated by the diesel engine: 90 W
Angular velocity of the engine: $ \dfrac{600}{\pi }rpm=(\dfrac{600}{\pi }\times \dfrac{2\pi }{60})rad/\sec =20rad/\sec $
As we know torque exerted by a body can be expressed as the ratio of the power generated by it and its angular velocity. i.e.
\[Torque=\dfrac{Power}{Angular\text{ }velocity}\]
\[\Rightarrow Torque=\dfrac{p}{\omega }\]

\[\Rightarrow Torque=\dfrac{90}{40}\]
Therefore the torque that the diesel engine can exert at the angular speed
\[\tau =4.5N-m\]

So, the correct answer is “Option A”.

Note: One is advised to also remember the relation between Torque and the angular displacement of an object which could be defined as the mechanical work applied during the rotation is the Torque times the rotation angle i.e. W and from this we derive the formula of instantaneous power of an acceleration body which is torque times the angular velocity P.