Question

Two identical particles each of mass 'm' start moving towards each other from rest from infinite separation under gravitational attraction. Their relative velocity of approach at separation 'r' is

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

Answer 1

Answer: (C)

$2\sqrt\frac{Gm}{r}$

Answer 2

From conservation of energy $\frac{GMm}{r} = \frac{1}{2} m \nu^2 + \frac{1}{2} m \nu^2$ relative velocity = $2 \times \nu$