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Standard XII

Physics

Gravitational Field

Two bodies of...

Question

Two bodies of masses $m_{1}$ and $m_{2}$ are initially at rest placed infinite distance apart. They are then allowed to move towards each other under mutual gravitational attraction. Their relative velocity when they are r distance apart is

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Solution

The correct option is A

From conservation of mechanical energy : decrease in gravitational potential energy = increase in kinetic energy.

or $\frac{G m_{1} m_{2}}{r} = \frac{1}{2} μ v_{r}^{2}$

Here, $μ = \frac{m_{1} m_{2}}{m_{1} + m_{2}}$ = reduced mass

and $v_{r}$ = relative velocity of approach

$∴$ $v_{r} = \sqrt{\frac{2 G (m_{1} + m_{2})}{r}}$

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