Three equal masses (each m) are placed at the corners of an equilateral triangle of side `a`. Then the escape velocity of an object from the circumcentre P of triangle is

Options

A. `sqrt((2 sqrt(3)Gm)/(a))`
B. `sqrt((sqrt(3)Gm)/(a))`
C. `sqrt((6sqrt(3)Gm)/(a))`
D. `sqrt((3 sqrt(3)Gm)/(a))`

Answer

C

Explanation

`(-"Gmm.")/(r) xx 3 + (1)/(2) m.v_(e)^(2) = 0 " or " (- 3Gm)/(((a)/(2)//cos 30^(@))) + (1)/(2) v_(e)^(2) = 0 `
`v_(e) sqrt((6 sqrt(3)Gm)/(a)).`