Four identical particles of equal masses 1 kg made to move along the circumference of a circle of radius 1 m under the action of their own mutual gravitational attraction. The speed of each particle will be
A) (1+22)G 2
B)G(1+22)
C)G2(22−1)
D)G2(1+22)
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The correct option is A) (1+22)G 2
explaination::
By resolving force F2, we get
F1 + F2 cos 45° + F2 cos 45° = Fc
F1 + 2F2 cos 45° = Fc
Fc = centripetal force = MV2 / R
GM2(2R)2=2GM2(2R)2cos45o=MV2R
GM24R2+2GM222R2=MV2R
GM24R2+GM2R=V2
V=GM4R+GM2R
V=12GMR[1+22]
now, mass=1kg and radius=1m
⇒V=12G(1+22)
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