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)

Engineering

Physics

Escape and Orbital Velocity

Question

The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is 4 $\sqrt{\frac{GM}{L}}$

The energy of the mass m remains constant

The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is $\sqrt{\frac{2 GM}{L}}$

The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is 2 $\sqrt{\frac{GM}{L}}$

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$\frac{GMm}{L} \times 2 = \frac{1}{2} {mv}^{2}$

$v = 2 \sqrt{\frac{am}{L}}$

energy of system is constant, not of the mass m