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Satellites

The ratio of ...

Question

The ratio of distances of satellites A and B from the center of the earth is 1.4:1, then the ratio energies of satellites B and A will be-

A

1.4 : 1

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B

2 : 1

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C

1 : 3

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D

4 : 1

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Solution

The correct option is C $1.4 : 1$
Given,
$r_{A} : r_{B} = 1.4 : 1$
The total mechanical energy of the satellite will be
$E = - \frac{G M m}{2 r}$
$E \propto \frac{1}{r}$
ratio, $\frac{E_{B}}{E_{A}} = \frac{r_{A}}{r_{B}} = \frac{1.4}{1}$
$E_{B} : E_{A} = 1.4 : 1$
The correct option is A.

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