First slide

Gravitaional potential energy

Question

Two bodies of masses m₁ and m₂, are initially at rest at infinite distance apart. They are then allowed to move towards each other under mutual gravitational attraction. Their relative velocity of approach at a separation distance r between them is

Moderate

A

${[2 G \frac{(m_{1} - m_{2})}{r}]}^{1 / 2}$
B

${[2 G \frac{(m_{1} + m_{2})}{r}]}^{1 / 2}$
C

${[\frac{r}{2 G (m_{1} m_{2})}]}^{1 / 2}$
D

${[2 \frac{G}{r} m_{1} m_{2}]}^{1 / 2}$

Solution

$v_{1} = \sqrt{(\frac{2 {Gm}_{1}}{r})} and v_{2} = \sqrt{(\frac{2 {Gm}_{2}}{r})}$
$(∵$ velocity of each is equal to escape velocity w.r.t. each other)
relative velocity $(v_{1} - v_{2}) = v$
or $V = \sqrt{\{\frac{2 G (m_{1} + m_{2})}{r}\}}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App