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Q.

Four similar particles of mass m are orbiting in a circle of radius r in the same angular direction because of their mutual gravitational attractive force. Velocity of a particle is given by

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a

Gmr1+22412

b

Gmr3

c

Gmr(1+22)

d

12Gmr1+22212

answer is A.

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Detailed Solution

Centripetal force = net gravitational force⇒ mv02r=2Fcos45∘+F1=2Gm2(2r)212+Gm24r2         mv02r=Gm24r2[22+1]⇒ v0=Gm(22+1)4r12
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Four similar particles of mass m are orbiting in a circle of radius r in the same angular direction because of their mutual gravitational attractive force. Velocity of a particle is given by