Gravitation

JEE Main level, single correct, medium

195 of 223

Question 195 of 223

A satellite is revolving in a circular orbit at a height hh from the earth's surface (radius of earth RR; h\lt\ltR\text{h}\text{\lt \lt }\text{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.)

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Answer: (B) gR(2−1)\sqrt{gR}\left(\sqrt{2}-1\right)

Since, h\lt\ltR\text{h}\text{\lt \lt }\text{R},

Ve=2gR{V}_{e}=\sqrt{2gR}

& V0=gR{V}_{0}=\sqrt{gR}

∴∴The minimum increase in velocity required,

Ve−V0=2gR−gR{V}_{e}-{V}_{0}=\sqrt{2gR}-\sqrt{gR}

=(2−1)gR=\left(\sqrt{2}-1\right)\sqrt{gR}

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