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A uniform rod P Q of length l and mass m is placed on a smooth horizontal surface. It is hinged at one of its ends and touches the conducting circular loop at another end. The system is subjected to vertical magnetic field B 0 . Rod is given angular velocity ω 0 about the axis passing through P . If the time after which its angular velocity becomes half is a b m R l n 2 B 2 l 2 . Find the value of a + b , where a and

Correct answer

7

Step-by-step solution

ε = 1 2 B 0 ω l 2 I = 1 2 B 0 ω l 2 R τ = I l 2 B 0 4 = 1 4 B 0 ω l 2 R l 2 B 0 B 0 2 ω l 4 R = m l 2 3 d ω d t 3 B 2 l 2 4 m R t = - ∫ d ω d t t = 4 m R l n 2 3 B 2 l 2 ∴ a = 4   and b = 3 ⇒ a + b = 4 + 3 = 7

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