A wheel with radial metal spokes 1 m in length is rotated in a magnetic field of `0.5 xx 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

Options

A. 400
B. 500
C. 600
D. 700

Answer

A

Explanation

Induced emf between rim and axle of wheel
`= (1)/(2) B omega R^(2)`
So, `(pi)/(3000) = (1)/(2) xx 0.5 xx 10^(-4) xx w xx 1^(2)`
`rArr omega = (2 xx pi)/(3000 xx 0.5 xx 10^(-4))`
`= (2pi xx 10000 xx 2)/(3000)`
`rArr` Rotation frequency in rounds per minute
`= (10000 xx 2)/(3000) xx 60`
= 400 rpm