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JEE Main 20163 April
Exam
JEE Main
Year
2016
Date
3 April
Subject
Physics
Chapter
Gravitation

JEE Main 2016 · 3 April · Physics · Gravitation

A satellite is revolving in a circular orbit at a height h from the...

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

Options

  1. AgR2\sqrt{\dfrac{gR}{2}}
  2. BgR(2−1)\sqrt{gR}\left(\sqrt{2} - 1\right)
  3. C2gR\sqrt{2gR}
  4. DgR\sqrt{gR}

Correct answer

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

Step-by-step solution

Since,& h<<R\text{h} \text{<<} \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}

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