Q .     A thin uniform annular disc (see figure) of mass M has outer radius 4R and inner radius 3R. The work required to take a unit mass from point P on its axis to infinity is

JEE 2010 ADVANCED Paper 1
A

`\frac{2GM}{7R}(4\sqrt{2}-5)`

B

`-\frac{2GM}{7R}(4\sqrt{2}-5)`

C

`\frac{GM}{4R}`

D

`\frac{2GM}{5R}(\sqrt{2}-1)`

HINT

We know that the work required to take a unit mass from P to infinity `=-V_p`, where `-V_p` is the gravitational potential at P due to the disc. To find `V_p`, we divide the disc into small elements, each of thickness dr. Consider one such element at a distance r from the center of the disc as shown. Mass of the element `dm=\frac{M(2\pi r dr)}{\pi(4R)^2-\pi(3R)^2}`

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