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Satellites

An artificial...

Question

An artificial satellite is revolving round the earth in a circular orbit. Its velocity is half the escape velocity. Its height from earth's surface is

A

6400 k m

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B

12800 k m

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C

3200 k m

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D

1600 k m

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Solution

The correct option is A $6400 k m$
Orbital velocity of the artificial satellite
$v_{0} = R \sqrt{\frac{g}{R + h}}$
Escape velocity $v_{c} = \sqrt{2 g R}$
Given, $v_{0} = \frac{1}{2} v_{c}$
$\frac{1}{2} \sqrt{2 g R} = R \sqrt{\frac{g}{R + h}}$
$\frac{1}{\sqrt{2}} = \sqrt{\frac{R}{R + h}}$
or $R + h = 2 R$
$h = R = 6400 k m$ .

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