A point particle is held on the axis of a ring of mass m and radius r at a distance r from its centre C . When released, it reaches C under the gravitational attraction of the ring. Its speed at C wil

Question

A point particle is held on the axis of a ring of mass m and radius r at a distance r from its centre C . When released, it reaches C under the gravitational attraction of the ring. Its speed at C will be

TestHub · Accepted Answer

Let ' M ' be the mass of the particle Now, E initial ​ = E final ​ i.e. 2 ​ r GMm ​ + 0 = r GM m ​ + 2 1 ​ M V 2 ​ or, 2 1 ​ M V 2 = r GM m ​ [ 1 − 2 ​ 1 ​ ] ⇒ 2 1 ​ V 2 = r G m ​ [ 1 − 2 ​ 1 ​ ] or, V = r 2 G m ​ ( 1 − 2 ​ 1 ​ ) ​ ​

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