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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

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$\frac{2 G M}{5 R} (\sqrt{2} - 1)$

$\frac{G M}{2 R}$

$- \frac{2 G M}{7 R} (4 \sqrt{2} - 5)$

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

answer is A.

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Detailed Solution

$\begin{array}{l} dm = \frac{M (2 πr) dr}{π (16 R^{2} - 9 R^{2}) 4 R} \\ dV = \frac{- G (dm)}{\sqrt{r^{2} + 16 R^{2}}}; V = \int_{3 R}^{4 R} dV \\ W = m [V_{\infty} - V] \end{array}$

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