Two bodies, each of mass M, are kept fixed with a separation 2L. A particle of mass m is projected from the midpoint of the line joining their centres, perpendicular to the line. The gravitational constant is G. The correct statement (s) is (are)

Options

A. The minimum initial velocity of the mass m to escape the gravitational field of the two bodies in `4sqrt((GM)/(L))`
B. The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is `2sqrt((GM)/(L))`
C. The minimum initial velocity of the mass m t eacape the gravitational field of the two bodies is `sqrt((2GM)/(L))`
D. The energy of the mass m remains constant

Answer

B

Explanation

(b) `(1)/(2)mv^2 =2[(GMm)/(L) rArr v =2sqrt((GM)/(L))`
The potential energy is a combined property of the three
mass system. The kinetic energy of mass m is only its energy
which decreasese as it moves.
(b) is the correct option.