Two particles of combined mass M, placed in space with certain separation are released interaction between the particles is only of gravitational nature and there is no external force present. Acceleration of one particle with respect to the other when separation between them is R, has a magnitude :

Options

A. `(GM)/(2R^(2))`
B. `(GM)/(R^(2))`
C. `(2GM)/(R^(2))`
D. not possible to calculate due to lack of information

Answer

B

Explanation

`a_(1)=(GM_(1)M_(2))/(R^(2))//M_(1)`
`a_(2)=(GM_(1)M_(2))/(R^(2))//M_(2)`
acceleration of `M_(1)` w.r.t `M_(2)`
`a_("rel") =a_(1)+a_(2)=(G(M_(1)+M_(2)))/(R^(2))=(GM)/(R^(2))`