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 cehntres, perpendicualr 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 is `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 to escape the gravitational field of the two bodies is `sqrt((2GM)/L)`
D. The energy of the mass m remains constant.

Answer

B, D

Explanation

The situation is as shown in the figure
Applying the conservation of mechanical energy ,

`-(GMm)/L-(GMm)/L +1/2mv^2 =0+0`
`1/2mv^2 = (2GMm)/L rArr v=sqrt((4GM)/L)=2sqrt((GM)/L)`
The energy of mass m will remain conserved hence option (d) is also correct.