A very long $π$ shaped railing made of resistanceless conducting wire is kept fixed in vertical plane. A uniform rod of mass ' $m$ ' and resistance $R$ is released from rest in horizontal position as shown in figure. The rod is always in contact with $π$ shaped railing at two points distant $l$ apart. A uniform and constant magnetic field $B$ exists in space normal to the plane of the railing as shown in figure. Find the maximum work done (in joules) by all the forces on the rod.
$(T a k e m = \frac{1}{2} k g, R = 10 Ω, l = \frac{1}{2} m, B = 10 T a n d g = 10 m / s^{2})$

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Detailed Solution

$\frac{B^{2} l^{2} v}{R} = m g \Rightarrow v = \frac{m g R}{B^{2} l^{2}} = \frac{0.5 \times 10 \times 10}{100 \times 0.25} = 2 m / s W = \frac{1}{2} m v^{2} = 1 J$

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