Question

A metallic rod of $1 \,m$ length is rotated with a frequency of $50$ revolution per second, with one end hinged at the centre and the other end at the circumference of a circular metallic ring of radius $1\, m$ about an axis passing through the centre and perpendicular to the plane of the ring. $A$ constant uniform magnetic field of $1 \,T$ parallel to the axis is present everywhere. The emf between the centre and the metallic ring is

• A. $157\,V$
• B. $117\,V$
• C. $127\,V$
• D. $137\,V$

Answer 1

Answer: (A)

$157\,V$

Answer 2

Formula for $E$ is $E =\frac{1}{2} B \omega l ^{2}$ $=\frac{1}{2} \times 2 \pi \times 50 \times 1 \times 1 \times 2$ $=50 \pi$ $=157 \,V$