Question:
An automobile engine develops $100 \,kW$ power when rotating at a speed of $1800\, rpm$. The torque delivered by the engine is
An automobile engine develops $100 \,kW$ power when rotating at a speed of $1800\, rpm$. The torque delivered by the engine is
Updated On: Jul 6, 2022
- $\frac{10^{2}}{6\pi} \,N \,m$
- $\frac{10^{4}}{6\pi} \,N \,m$
- $\frac{10^{6}}{6\pi} \,N \,m$
- $\frac{10^{8}}{6\pi} \,N \,m$
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The Correct Option is B
Solution and Explanation
Here, $P = 100 \,kW $
$ = 100\times10^{3} W = 10^{5}W $
$ \upsilon = 1800 \,rpm = \frac{1800}{60}\, rps = 30 \,rps $
$ \therefore\omega = 2 \,\pi \,\upsilon =2\pi \left(30\right) = 60 \pi \,rad \,s^{-1}$
As $P= \tau\omega $
$\therefore\tau = \frac{p}{\omega} = \frac{10^{5} W}{60 \pi \,rad \,s^{-1}} $
$ = \frac{10^{4}}{6\pi} \,N \,m$
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Concepts Used:
System of Particles and Rotational Motion
- The system of particles refers to the extended body which is considered a rigid body most of the time for simple or easy understanding. A rigid body is a body with a perfectly definite and unchangeable shape.
- The distance between the pair of particles in such a body does not replace or alter. Rotational motion can be described as the motion of a rigid body originates in such a manner that all of its particles move in a circle about an axis with a common angular velocity.
- The few common examples of rotational motion are the motion of the blade of a windmill and periodic motion.