First slide

Gravitaional potential energy

Question

Two satellites of the same mass are launched in the same orbit around the earth so as to rotate opposite to each other. If they collide inelastically and stick together as wreckage, the total energy of the system just after collision is

Moderate

A

$- \frac{2 G M m}{r}$
B

$- \frac{G M m}{r}$
C

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

$\frac{G M m}{4 r}$

Solution

Energy of each satellite in the orbit $\frac{- G M m}{2 r}$
Total energy of the system before collision,
$E_{i}$ = $E_{1}$ = $E_{2}$ = 2E = -2 × $\frac{G M m}{2 r} = - \frac{G M m}{r}$
As the satellites of equal mass are moving in the opposite directions and collide inelastically, the velocity of the wreckage just after the collision is
mv - mv = 2mV, i.e., V = 0
The energy of the wreckage just after the collision will be totally potential and will be
$E_{f} = \frac{G M (2 m)}{r} = - \frac{2 G M m}{r}$

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