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Consider two satellites A and B of equal mass m, moving in same circular orbit about earth, but in opposite sense as shown in the figure. The orbital radius is r. The satellites undergo a collision which is perfectly inelastic. For this situation mark out the correct statement(s). [take mass of the earth as M>>m and ignore the gravitational interaction between the satellites]

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The total energy of the two satellites plus earth system just before collision is $- \frac{G M m}{r}$

The total energy of the two satellite plus the earth system just after collision is $- \frac{2 G M m}{r}$

The total energy of two satellite plus earth system just after collision is $- \frac{G M m}{2 r}$

The combined mass (two satellites) will fall towards the earth just after collision.

answer is A, B, D.

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Detailed Solution

Just before collision, the total energy of two satellites is, $E = - \frac{G M m}{2 r} - \frac{G M m}{2 r} = - \frac{G M m}{r}$

Let orbital velocity is v, then from momentum conversation,

mv-mv= $2 m \times v_{1}$

$v_{1} = 0$

As velocity of combined mass just after collision is zero, the combined mass will fall towards earth. At this instant, the total energy of the system only consists of the gravitational potential energy given by

$U = - \frac{G M \times 2 m}{r}$

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