Question

An automobile engine develops $100 \,kW$ power when rotating at a speed of $1800\, rpm$. The torque delivered by the engine is

• A. $\frac{10^{2}}{6\pi} \,N \,m$
• B. $\frac{10^{4}}{6\pi} \,N \,m$
• C. $\frac{10^{6}}{6\pi} \,N \,m$
• D. $\frac{10^{8}}{6\pi} \,N \,m$

Answer 1

Answer: (B)

$\frac{10^{4}}{6\pi} \,N \,m$

Answer 2

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 $P= \tau\omega$ $\therefore\tau = \frac{p}{\omega} = \frac{10^{5} W}{60 \pi \,rad \,s^{-1}}$ $= \frac{10^{4}}{6\pi} \,N \,m$