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A conducting loop is placed in a magnetic field of strength $B$ perpendicular to its plane. Radius of the loop is $r$ , current in the loop is $i$ and linear mass density of the wire of loop is $m$ . Speed of any transverse wave in the loop will be

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$\sqrt{\frac{2 B i r}{m}}$

$\sqrt{\frac{B i r}{2 m}}$

$2 \sqrt{\frac{B i r}{m}}$

$\sqrt{\frac{B i r}{m}}$

answer is A.

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Detailed Solution

$F = B i l 2 T \sin \frac{θ}{2} = F 2 T (\frac{θ}{2}) = B i (r θ) T = B i r$

Now speed, $v = \sqrt{\frac{T}{m}} = \sqrt{\frac{B i r}{m}}$

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