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 f - Physics MCQ JEE Main 2026 | ExamTest.live

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A metallic rod of length l is tied to a string of length 2 l 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:

Solution & Step-by-step Explanation

The induced EMF in a rotating rod is given by \int B v d x .The rod extends from distance x = 2 l to x = 3 l from the center of rotation.Velocity at distance x is v = ω x . e = \int_{2 l}^{3 l} B (ω x) d x = B ω [\frac{x ^{2}}{2}]_{2 l}^{3 l} e = \frac{B ω}{2} [(3 l)^{2} - (2 l)^{2}] = \frac{B ω}{2} [9 l^{2} - 4 l^{2}] = \frac{5 B ω l ^{2}}{2} .

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A metallic rod of length l is tied to a string of length 2 l 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:

\frac{3B\omega l^2}{2}

\frac{4B\omega l^2}{2}

\frac{5B\omega l^2}{2}

\frac{2B\omega l^2}{2}

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