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Question

A particle starts from rest at a distance R from the centre and along the axis of a fixed ring of radius R & mass M. Its velocity at the centre of the ring is:
1279706_cf5fd49188a14907a43514a75f542ad6.png

A
2GMR
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B
2GMR
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C
(22)GMR
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D
(22)GMR
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Solution

The correct option is C (22)GMR
Applying conservation of energy
v=G×Mx2+R2
Potential energy=v×m=GmMx2+R2
Initial kinetic energyri=0
Potential energy at center=GMmR{x=0}
GMmx2+R2+0=GMmR+12mv2
12mv2=GMmRGMmx2+R2=GMm{1R1x2+R2}
v2=2GMmm{1R1x2+R2}
v2= (222)(GMR)=(22)GMR

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