Question

Two satellites of the same mass are lauched 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

• A. $-\frac{2GMm}{r}$
  
• B. $-\frac{GMm}{r}$
  
• C. $\frac{2GMm}{r}$
  
• D. $\frac{GMm}{2r}$
  
  

Answer 1

The correct option is A $-\frac{2GMm}{r}$


Since both the satellites are in a circular orbit of the same radius $r$, their velocities will be the same. $$v=\sqrt{\frac{GM}{r}}$$ Since, external forces along the tangential direction to the orbit are absent, so the linear momentum of the system along that direction (both satellites) will be conserved.

$mv-mv=mV+mV$

Where,$V$ is the final velocity of the system.

$\Rightarrow V=0$

So, the kinetic energy will become zero, and total energy will be contributed by potential energy alone.

So, $E=-\frac{GM(m+m)}{r}=-\frac{2GMm}{r}$

Hence, option (a) is the correct answer.