Question

Two particles each of mass $M$ are released from rest when they are at infinite separation. The velocity of any one when their separation becomes $r$ will be

• A. $\sqrt{\frac{2GM}{r}}$
• B. $\sqrt{\frac{GM}{r}}$
• C. $\sqrt{\frac{GM}{r}}$
• D. $2\sqrt{\frac{GM}{2r}}$

Answer 1

Answer: (C)

$Mv_1 - Mv_2 = 0$
$ ∴ v_1 = v_2 = v$
When separation becomes $r$ by using energy conservation
$-\frac{GMM}{r} +\frac{1}{2}Mv^{2} +\frac{1}{2}Mv^{2} = 0$
$ Mv^{2} = \frac{GMM}{r} $
$ v = \sqrt{\frac{GM}{r}}$