Question

Two satellites of same mass $m$ are launched in the same orbit (radius $r$) around the earth (mass $M$) so as to rotate opposite to each other. If they collide inelastically and stick together as wreakage, the total energy of the system just after collision is-

• A. $-\frac{GMm}{r}$
• B. $\frac{GMm}{2r}$
• C. $-\frac{2GMm}{r}$
• D. $\frac{GMm}{4r}$

Answer 1

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


Orbital speed ($v$) of both the satellites will be equal as radii are equal because $v=\sqrt{\frac{GM}{r}}$



On applying law of conservation of linear momentum just before and just after the collision we get,
$mv+m(-v)=2m{v}^{\prime }\Rightarrow v^{\prime }=0$

Hence, the satellites wreakage will be at rest just after the collision.

Therefore the total energy of the system will be only due to potential energy.
Total energy, $E=\frac{-GM\left(2m\right)}{r}$

$\Rightarrow E=-\frac{2GMm}{r}$