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# Three uniform spheres of mass M and radius R each are kept in such a way that each touches the other two. The magnitude of the gravitational force on any of the sphere due to the other two sphere is

$(a)\;\frac {\sqrt 3}{4}\frac{GM^2}{R^2} \quad (b)\;\frac{3}{2}\frac{GM^2}{R^2} \quad (c)\;\sqrt 3 \frac{GM^2}{R^2} \quad (d)\;\frac{\sqrt 3}{2} \frac{GM^2}{R^2}$

Force between two spheres will be
$F= \large\frac{GMM}{(2R)^2}=\frac{GM^2}{4R^2}$
Two forces of equal magnitude are acting at angle $60^{\circ}$ on any of the sphere
$F_{net}=\large\frac{\sqrt 3}{4} \frac{GM^2}{R^2}$
Hence a is the correct answer.

edited Feb 17, 2014 by meena.p