Gravitation Part 1

Let us consider the gravitational force acting on each mass M by adjacent particles be F.
and the gravitational force acting on each mass M diagonally be F1
The net force, Fnet=

Mv2

R

Along the centre of circle,
√2F+F1=

Mv2

R

√2(

GMM

(√2R)2

)+(

GMM

(2R)2

) =

Mv2

R

⇒

GM

R2

(

1

√2

+

1

4

)=

v2

R

⇒ v=

1

2

√

GM(2√2+1)

R

Hence, the speed of each particle is

1

2

√

GM(2√2+1)

R

.