Question

Two bodies, each of mass $M,$ are kept fixed at 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 $4\sqrt{\frac{GM}{L}}$
• B. The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is $2\sqrt{\frac{GM}{L}}.$
• C. The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is$\sqrt{\frac{2GM}{L}}$
• D. The energy of the mass m remains constant.

Answer 1

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

$\frac{-2GMm}{L}+\frac{1}{2}m{v}^2=0$

$\Rightarrow v=2\sqrt{\frac{GM}{L}}$

Note:
The energy of mass m means its kinetic energy (KE) only and not the potential energy of interaction between m and the two bodies (of mass M each) which is the potential energy of the system.