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JEE Main 20204 SeptemberEvening Shift
Exam
JEE Main
Year
2020
Date
4 September
Shift
Evening Shift
Subject
Physics
Chapter
Gravitation

JEE Main 2020 · 4 September · Evening Shift · Physics · Gravitation

A body is moving in a low circular orbit about a planet of mass M...

A body is moving in a low circular orbit about a planet of mass MM and radius RR. The radius of the orbit can be taken to be RR itself. Then the ratio of the speed of this body in the orbit to the escape velocity from the planet is:

Options

  1. A12\dfrac{1}{\sqrt{2}}
  2. B22
  3. C11
  4. D2\sqrt{2}

Correct answer

A. 12\dfrac{1}{\sqrt{2}}

Step-by-step solution

The orbital velocity of the body in an orbit of the radius RR is vo=GmR{v}_{o} = \sqrt{\dfrac{Gm}{R}}

The escape velocity from the surface is ve=2GmR{v}_{e} = \sqrt{\dfrac{2Gm}{R}}

Ratio, v0ve=GmR2GmR=12\dfrac{{v}_{0}}{{v}_{e}} = \dfrac{\sqrt{\dfrac{Gm}{R}}}{\sqrt{\dfrac{2Gm}{R}}} = \dfrac{1}{\sqrt{2}}

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