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A thin uniform annular disc of mass M has outer radius 4R and inner radius 3R. Find the work needed to move a unit mass from a point P on its axis, located at distance 4R from the centre, to infinity.

1. (2GM/(7R)) * (4*sqrt(2) - 5)
2. (GM/(4R))
3. (2GM/(5R)) * (sqrt(2) - 1)
4. (GM/(7R)) * (4*sqrt(2) - 5)

Correct answer: (2GM/(7R)) * (4*sqrt(2) - 5)

Solution

The axial potential of the annulus is found by integrating ring contributions from inner to outer radius; the required work is the magnitude of this potential at P (point at distance 4R on the axis).

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