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Physics

Mechanics

Easy

Question

The ratio of the K.E. required to be given to the satellite to escape earth's gravitational field to the K. E. required to be given so that the satellite moves in a circular orbit just above earth atmosphere is

One
Two
Half
Infinity

The correct answer is: Two

$1 half m v subscript e superscript 2 equals 1 half m open parentheses square root of fraction numerator 2 G M over denominator R end fraction end root close parentheses squared equals fraction numerator G M m over denominator R end fraction straight K. straight E. text required for satellite to move in circular orbit end text 1 half m v subscript 0 superscript 2 equals 1 half m open parentheses square root of fraction numerator G M over denominator R end fraction end root close parentheses squared equals fraction numerator G M n over denominator 2 R end fraction$
K.E. required for satellite to escape from earth's gravitational field

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$text Two satellites of masses end text m subscript 1 text and end text m subscript 2 open parentheses m subscript 1 greater than m subscript 2 close parentheses text are revolving round the earth in circular orbits end text text of radius end text r subscript 1 text and end text r subscript 2 open parentheses r subscript 1 greater than r subscript 2 close parentheses text respectively. Which of the following statements is true regarding end text text their speeds end text v subscript 1 text and end text v subscript 2 ?$

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