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

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) √(Gm/r) (B) √(2Gm/r) (C) 2√(Gm/r) (D) √(Gm/2r)

Tardigrade Admin · Accepted Answer

From conservation of energy (GMm/r) = (1/2) m ν2 + (1/2) m ν2 relative velocity = 2 × ν

Q. 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

$\frac{G m}{r}$

$\frac{2 G m}{r}$

$2 \frac{G m}{r}$

$\frac{G m}{2 r}$

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

Q. 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

rGm​​

r2Gm​​

2rGm​​