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

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

Answer 1

Answer: (A)

$-\frac{2GMm}{r}$

Let both the satellites are revolving in a circular orbit of radius r with velocity v in opposite direction.

Just before collision: initial momentum, $p_i=mv-mv=0$

Now as just after collision both the satellites stick together, so let the velocity of system be $v_f$

Thus according to Conservation of momentum law, final momentum ($P_f$) should be zero.

Thus $2m{v}_f=0⟹v_f=0$ i-e, after collision both satellites come to rest.Hence total energy of the system will be only total potential energy of the system.

Thus, $T.E=2P.E=2(\frac{-GMm}{r})$