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Two bodies, each of mass M, are kept fix...

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)

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.

Text Solution

Verified by Experts

The correct Answer is:
D

Total energy of m is conserved for escape velocity
`K.E_(f)+P.E_(f)+K.E_(i)+P.E_(i)`
`0+0=(1)/(2)mv^(2)+2[(-GM)/(L)]`
`impliesv=sqrt((4GM)/(L))=2sqrt((GM)/(L))`
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