Gravitation 2 Question 2
5. A satellite is revolving in a circular orbit at a height $h$ from the Earth’s surface (radius of earth $R, h«R$ ). The minimum increase in its orbital velocity required, so that the satellite could escape from the Earth’s gravitational field, is close to (Neglect the effect of atmosphere)
(2016 Main)
(a) $\sqrt{2 g R}$
(b) $\sqrt{g R}$
(c) $\sqrt{g R / 2}$
(d) $\sqrt{g R}(\sqrt{2}-1)$
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Answer:
Correct Answer: 5. (d)
Solution:
- $v _{\text {orbital }}=\sqrt{\frac{G M}{R}}=\sqrt{g R}$
$v _{\text {escape }}=\sqrt{2 g R}$
$\therefore$ Extra velocity required $=v _{\text {escape }}-v _{\text {orbital }}=\sqrt{g R}(\sqrt{2}-1)$
