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

Options

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

Answer

B

Explanation

Potential at centre `= -(4GM)/(r)=(-4GM)/(a//sqrt(2))=-(4sqrt(2)GM)/(a)`

Potential energy `= (-4sqrt(2)GMm)/(a)`
Binding energy `= (4 sqrt(2)GMm)/(a)`
`:. (1)/(2)mv_(e)^(2)=(4sqrt(2)GMm)/(a)or v_(e)=sqrt((8sqrt(2)GM)/(a))`.