Question

Two particle of equal mass m go around a Circle of radius R under the action of their mutual gravitational attraction . the speed of each particle with respect to their centre of mass is [AIEEE 2011] ​

Answer 1

Answer:

ANSWER

Given,

Masses of the two particles are m

1

=m

2

=m

And radius of the two particles are r

1

=r

2

=R

So ,The Gravitational force of attraction between the particles F=

R

2

G×m×m

−−−−−−−−(1)

Ans, centripital force F=

R

m×v

2

−−−−−−(2)

From given condition (1) and (2)

(2R)

2

Gmm

=

R

mv

2

,

v=

4R

Gm

=

2

1

R

Gm

So the speed of the each particle is v=

2

1

R

Gm

Explanation:

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Answer 2

Explanation:- As gravitational force provides necessary centripetal force .

i.e ., F = Gm² /(2R)² = mv² /R

⟹ v = √Gm/4R Answer