Discussion Forum



1)

Two bodies, each of mass M, are kept fixed with a separation of 2L. A particle of mass m is projected from the mid-point of the line joining their centres, perpendicular to the line.The  gravitational constant 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 remain constant

Answer:

Option B,D

Explanation:

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Let v is the minimum velocity .From energy conservation

 $U_{c}+K_{c}=U_{\infty}+K_{\infty}$

$\therefore$    $mV_{c}+\frac{1}{2}mv^{2}=0+0$  $  \therefore$   $ v=\sqrt{-2V_{c}}$

 = $\sqrt{(-2)\left(\frac{-2GM}{L}\right)}=2\sqrt{\frac{GM}{L}}$