Four equal masses (each of mass M) are placed at the corners of a squares side a the escape velocity of a body from the centre O of the square is

Options

A. `4sqrt(2GM)/(a)`
B. `sqrt(8sqrt(2GM))/(a)`
C. `(4GM)/(a)`
D. `sqrt(4sqrt(2)GM)/(a)`

Answer

B

Explanation

Potential at centre `=-(4GM)/(r )=(-4GM)/(a//sqrt(2))=-(4sqrt(2)GM)/(a)`
`PE=(-4sqrt(2)GMm)/(a)`
`BE=(4sqrt(2)GMm)/(a)`
`therefore 1/2mv_(e)^(2)=(4sqrt(2)GMm)/(a)`
`rarr v_(e )=sqrt(8sqrt(2)GM)/(a)`