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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(221)

D)G2(1+22)

 

 

 

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The correct option is A) (1+22)G 2 

explaination::

24-feb-physics-shift-1-question{from -byzus} 

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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