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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 cehntres, perpendicualr 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 `4 sqrt(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 mass `m` remains constant.

Text Solution

Verified by Experts

The correct Answer is:
B
Let `upsilon` be the minimum initial velocity of the mass `m` to escape. According to law of conservation of total energy, we have
`- (2GM m)/(L) + (1)/(2) m upsilon^(2) = 0`
or `upsilon^(2) = (4GM)/(L)` or `upsilon = 2sqrt((GM)/(L))`
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