A metallic rod of length ‘l’ is tied to a string of length 2l and made to rotate with angular speed ω 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

$fraction numerator 2 Bωl cubed over denominator 2 end fraction$
$fraction numerator 3 Bωl cubed over denominator 2 end fraction$
$fraction numerator 4 Bωl squared over denominator 2 end fraction$
$fraction numerator 5 Bωl squared over denominator 2 end fraction$

Solution

fraction numerator 5 Bωl squared over denominator 2 end fraction

de space equals space straight B space left parenthesis ωx right parenthesis. dx straight e space equals space Bω integral subscript 2 straight L end subscript superscript 3 straight L end superscript xdx space equals fraction numerator 5 BωL squared over denominator 2 end fraction

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