A metallic rod of length 'l' is tied to a string of length 2l and made to rotate with angular speed w on a horizontal table with one end of the string fixed. If there is a vertical magnetic field 'B' in the region, the e.m.f. Induced across the ends of the rod is

Options

A. `(2 B omega l^(2))/(2)`
B. `(3 B omega L^(2))/(2)`
C. `(5 B omega l^(2))/(2)`
D. `(4 B omega L^(2))/(2)`

Answer

C

Explanation

As shown in Fig.
`e = (d phi)/(dt) =(B dA)/(dt) = (B pi [(3 l)^(2) - (2 l)^(2)])/(1//n) = B pi n xx 5 l^(2)`
`e = B (2 pi n) xx (5)/(2) l^(2) = (5)/(2) B omegal^(2)`