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Two particles of equal mass m move aroun...

Two particles of equal mass m move around a circle of radius R under the influence of their mutual gravitational attraction, the speed of each particle with respect to their center of mass will be ..........

A

`sqrt((Gm)/(R))`

B

`sqrt((Gm)/(4R))`

C

`sqrt((Gm)/(3R))`

D

`sqrt((Gm)/(2R))`

Text Solution

Verified by Experts

The correct Answer is:
B
`implies` Centripetal force of any one particle = Gravitational force between two particles .

`mv^2 /R = (GMm)/((2R)^2)`
`(mv^2)/R =(GMm)/(4R_e^2)`
`:. v_2^2 =(GM)/(4R)`
`:.v = sqrt((GM)/(4R))`
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Knowledge Check

  • Four particles, each of mass M and equidistant "from each other, move along a circle of radius R under the action of the mutual gravitational attraction. The speed of each particle is ......... (G = universal gravitational constant)

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