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Q.

Three uniform spheres each having mass ‘m’ and radius ‘R’ kept in such a way that each two touches the other. The magnitude of the gravitational force on any sphere, due to the other two is

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a

\frac{\sqrt{3} Gm}{R^{2}}

b

\frac{\sqrt{3} Gm}{{2R}^{2}}

c

\frac{\sqrt{3} {Gm}^{2}}{4 R^{2}}

d

\frac{{Gm}^{2}}{4 R^{2}}

answer is A.

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Detailed Solution

Question Image

$Resultant force = \sqrt{F^{2} + F^{2} + 2 F^{2} \cos 60 °}$

$= \sqrt{3} F$

$= \sqrt{3} \frac{{Gm}^{2}}{{4R}^{2}}$ $[∴ F = \frac{Gm \times m}{{(2R)}^{2}}]$

$= \frac{\sqrt{3}}{4} \frac{{Gm}^{2}}{R^{2}}$

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