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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.)

1. √gR/2
2. √gR(√2−1)
3. √2gR
4. √gR

Correct answer: √gR(√2−1)

Solution

The correct option, √gR(√2−1), represents the additional velocity needed for the satellite to reach escape velocity from its current orbital speed. This is derived from the difference between the escape velocity and the orbital velocity at that height, considering the gravitational force acting on the satellite.

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