Two bodies, each of mass M , are kept fixed with a separation of 2 L . A particle of mass m is projected…

Two bodies, each of mass M, are kept fixed with a separation of 2L. A particle of mass m is projected from the midpoint of the line joining their centers, perpendicular to the line. The gravitational constant is G. The correct statement (s) is (are) :
  1. The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is 4GML.
  2. The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is 2GML.
  3. The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is 2GML.
  4. The energy of the mass m remains constant.

Solution

Applying mechanical energy conservation,

Ui+KEi=Uf+KEf
-GMmL×2+12mv2=0+0
⇒v=4GML

⇒v= 2GML

Asked in: JEE Advanced 2013 (Paper 2)

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