Four particles, each of mass M and equidistant from each other, move along a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle is:

Options

A. `(GM)/(R )`
B. `sqrt(2sqrt(2)(GM)/(R ))`
C. `sqrt((GM)/(R)(2sqrt(2) + 1))`
D. `sqrt((GM)/(R)(2sqrt(2) + 1)/(4))`

Answer

D

Explanation

Net force on `P` towards centre
`F = sqrt(2) F_(1) + F_(2)`
`:. (mnu^(2))/(R)= sqrt(2) [(G.MM)/(a^(2))] + (GMM)/((2R )^(2))`
or `nu^(2)/(R ) = (sqrt(2) GM)/(sqrt(2) R)^(2) + (GM)/(4R^(2))`
`:. nu = sqrt((GM)/(R ) (2sqrt(2) + 1)/(4))`