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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

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$\frac{4 B ω l^{2}}{2}$

$\frac{3 B ω l^{2}}{2}$

$\frac{2 B ω l^{2}}{2}$

$\frac{5 B ω l^{2}}{2}$

answer is D.

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Detailed Solution

$E = \int_{x = 21}^{31} B (X ω) d x = \frac{5 B l^{2} ω}{2}$

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