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Q.

A system consists of a thin ring of radius ‘R’ and a very long uniform wire oriented along axis of the ring with one of its ends coinciding with the centre of the ring. If mass of ring is ‘m’ and the linear mass density of the wire is $λ$ , then the interaction force between the ring and the wire is $F = \frac{K G m λ}{R}$ . Then find the value of ‘k’

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Detailed Solution

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$F = \int_{0}^{\infty} \frac{G M x}{{(R^{2} + x^{2})}^{3 / 2}} λ d x$

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A system consists of a thin ring of radius ‘R’ and a very long uniform wire oriented along axis of the ring with one of its ends coinciding with the centre of the ring. If mass of ring is ‘m’ and the linear mass density of the wire is λ, then the interaction force between the ring and the wire is F=KGmλR. Then find the value of ‘k’