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Variation of G Due to Height and Depth

A space shutt...

Question

A space shuttle is launched in a circular orbit near the earth's surface. The additional velocity be given to the space - shuttle to get free from the influence of gravitational force, will be.

A

1.52 k m / s

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B

2.75 k m / s

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C

3.28 k m / s

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D

5.18 k m / s

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Solution

The correct option is C $3.28 k m / s$
Orbital velocity of satellite revolving near earth's surface, $v = \sqrt{\frac{G M}{R}}$
$v = \sqrt{g R}$ (using $G M = g R^{2}$ )
$v = \sqrt{9.8 \times 6400 \times 1000}$
$⟹ v = 7.919 k m / s$
Escape velocity $v_{e} = \sqrt{2 g R} = \sqrt{2 (9.8) (6400 \times 1000)} = 11.2 k m / s$
Thus additional velocity required $= 11.2 - 7.919 k m / s = 3.28 k m / s$

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