Two particles of equal mass m go around a cir | vedclass

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Question

(B) The two particles of mass $m$ are separated by a distance $d = 2R$ because they move in a circle of radius $R$ around their common centre of mass.

Vedclass · Accepted Answer

$\sqrt{\frac{Gm}{4R}}$

Vedclass · Answer

(B) The two particles of mass $m$ are separated by a distance $d = 2R$ because they move in a circle of radius $R$ around their common centre of mass.The gravitational force between them is $F_G = \frac{G m^2}{(2R)^2} = \frac{G m^2}{4R^2}$.This gravitational force provides the necessary centripetal force for each particle to move in a circle of radius $R$. The centripetal force is $F_c = \frac{m v^2}{R}$.Equating the two forces: $\frac{m v^2}{R} = \frac{G m^2}{4R^2}$.Solving for $v$: $v^2 = \frac{G m^2}{4R^2} \cdot \frac{R}{m} = \frac{Gm}{4R}$.Therefore,$v = \sqrt{\frac{Gm}{4R}}$.

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 particle with respect to their centre of mass is

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