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Question

# A ring of mass m1 and radius R is fixed in space at some location. An external agent brings a point mass m2 from infinity to the centre of the ring. Work done by the external agent will be

A
Gm1m2R
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B
Gm1m2R
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C
Gm1m22R
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D
Gm1m22R
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Solution

## The correct option is A −Gm1m2RWork done will be equal to the change in the potential energy of the ring and mass system. When mass m2 is at infinity, Initial potential energy, Ui=0 When mass m2 is at centre of ring, Final potential energy, Uf=−Gm1m2R So, external work done, W=ΔU=Uf−Ui=−Gm1m2R−0=−Gm1m2R Hence, option (a) is the correct answer. ​​​​ Why this question? The gravitational potential of a ring of radius R and mass M at a distance r from its centre on the axis is given by V=−GM√R2+r2;0≤r≤∞

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