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Question
Four particles, each of mass M and equidistant from each other, move along a circle of radius R under the action of their mutual gravitational attraction. Calculate the speed of each particle.
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Solution
Force acting on a particle
= `"GM"^2/(2"R")^2 + "GM"^2/(("R"/sqrt2)^2) cos 45° + "GM"^2/(("R"/sqrt2)^2) cos 45°`
E = `"GM"^2/"R"^2 [1/4 + 1/sqrt2]`
Since particle, moving circular path experience centripetal force,
E = `"MV"^2/"R"`
`"MV"^2/"R" = "GM"^2/"R"^2 [1/4 + 1/sqrt2]`
∴ V = `1/2 sqrt("GM"/"R" (1 + 2sqrt2))`
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