Two satellites of mass $m$ are revolving round of earth ( mass $M$ ) in the same orbit of radius $r$ . Rotational directions of the two are opposite therefore, they can collide. Total mechanical energy of the system is

\frac{G M m}{2 r}

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\frac{- G M m}{r}

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

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Solution

The correct option is C $\frac{- 2 G M m}{r}$
According to the law of conservation of momemtum, the velocity of the system after collision, $V = 0$
$m (v) + m (- v) = (2 m) V = V = 0 (C o l l i s i o n$ is perfectly inelastic).
$∴$ After collision, the energy will be totally potential energy.
$E = \frac{- G M (2 m)}{r} = \frac{- 2 G M m}{r}$

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Two satellites of mass m are revolving round of earth ( mass M) in the same orbit of radius r. Rotational directions of the two are opposite therefore, they can collide. Total mechanical energy of the system is

The correct option is C −2GMmrAccording to the law of conservation of momemtum, the velocity of the system after collision, V=0m(v)+m(−v)=(2m)V=V=0 (Collision is perfectly inelastic).∴ After collision, the energy will be totally potential energy.E=−GM(2m)r=−2GMmr

Two satellites of mass $m$ are revolving round of earth ( mass $M$ ) in the same orbit of radius $r$ . Rotational directions of the two are opposite therefore, they can collide. Total mechanical energy of the system is