A ring of mass \( M=90 \) gram and radius \( R=3 \) meter is kept on a frictionless horizontal s...

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A ring of mass \( M=90 \) gram and radius \( R=3 \) meter is kept on a frictionless horizontal surface such that its plane is parallel to horizontal plane. A particle of mass \( m=10 \) gram is placed in contact with the inner surface of ring as shown figure. An initial velocity \( v=\sqrt{2} \mathrm{~m} / \mathrm{s} \) is given to the particle along the tangent of the ring. Find the magnitude of the force of interaction (in milli-newton) between the particle and ring.
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