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Consider the arrangement shown in figure. A thin rod (mass M and length 4R) and a sphere of equal mass M and radius R are located as shown in figure. The centre of the sphere being at a distance 2R from the centre of the rod on its perpendicular bisector. Assume that the system of rod and sphere is in gravity free space. If the force acting on the rod due to sphere is given by $\frac{G M^{2}}{\sqrt{n} R^{2}},$ find value of n.

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Detailed Solution

$F = \int_{0}^{2 R} \frac{G M^{2} d x}{{(x^{2} + 4 R^{2})}^{\frac{3}{2}}} = \frac{G M^{2}}{4 \sqrt{2} R^{2}}$

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