Question

A wheel with radial metal spokes $1m$ in length is rotated in a magnetic field of $0.5\times 10^{-4}T$ normal to the plane of the wheel. If the induced emf between the rim and axle is $\pi /3000V$, then the rotational speed of the wheel in revolutions per minute is

• A. 400
• B. 500
• C. 600
• D. 700

Answer 1

Answer: (A)

Induced emf between rim and axle of wheel
$=\frac{1}{2}B\omega R^2$
So, $\frac{\pi }{3000}=\frac{1}{2}\times 0.5\times 10^{-4}\times w\times 1^2$
$\Rightarrow \omega =\frac{2\times \pi }{3000\times 0.5\times 10^{-4}}$
$=\frac{2\pi \times 10000\times 2}{3000}$
$\Rightarrow$ Rotation frequency in rounds per minute
$=\frac{10000\times 2}{3000}\times 60$
$=400rpm$