Question

A wheel with radial metal spokes $1\, m$ 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 $\pi / 3000\, V$, 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
$=\frac{10000 \times 2}{3000} \times 60$
$=400\, rpm$