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Q. Two particles of equal mass $'m'$ go around a circle of radius $R$ under the action of their mutual gravitational attraction. The speed of each partial with respect to their centre of mass is :

AIEEEAIEEE 2011Gravitation

Solution:

$\frac{Gm^{2}}{\left(2R\right)^{2}} = m\omega^{2}R$
$\frac{Gm^{2}}{4R^{3}} = \omega^{2}$
$\omega = \sqrt{\frac{Gm}{4R^{3}}}$
$v = \omega R$
$v = \sqrt{\frac{Gm}{4R^{3}}}\times R\quad\quad= \quad\quad \sqrt{\frac{Gm}{4R}}$

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