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A ring has a total mass M but non-unifor...

A ring has a total mass `M` but non-uniformly distributed over its circumference. The radius of the ring is `R`. A point mass `m` is placed at the centre of the ring. Workdone in taking away this point mass from ecntre to infinity is

A

`-(GMm)/(R )`

B

`(GMm)/(R )`

C

`-(GMm)/(2R)`

D

`(GMm)/(R )`

Text Solution

Verified by Experts

The correct Answer is:
B
Gravitational potential at the centre of the ring even if mass is non-uniformly distributed on ring
is `V_(c ) = - (GM)/(R )`
Gravitational potential at infiity is, `V_(f) = 0`
Workdone = increase in potential energy
`= m(V_(f) - V_(c )) = m[0 - (-(Gm)/(R ))] = (GMm)/(R )`
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