By what percent the energy of a satellite has to be increased to shift it from an orbit of radius r to $\frac{3}{2} r$ ?

66.7%

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33.3%

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15%

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20.3%

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Solution

The correct option is B
33.3%

Binding energy of satellite in the first case in $\frac{G M m}{2 r}$ and in the second case is $\frac{G M m}{3 r}$

Energy increased

$△ E = \frac{G M m}{r} (\frac{1}{2} - \frac{1}{3}) = \frac{G M m}{6 r}$

$∴$ % increase = $\frac{\frac{G M m}{6 r}}{\frac{G M m}{2 r}} \times 100 = 33.33$

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By what percent the energy of a satellite has to be increased to shift it from an orbit of radius r to 32r?

The correct option is B 33.3% Binding energy of satellite in the first case in GMm2r and in the second case is GMm3r Energy increased △E=GMmr(12−13)=GMm6r ∴ % increase = GMm6rGMm2r×100=33.33

By what percent the energy of a satellite has to be increased to shift it from an orbit of radius r to $\frac{3}{2} r$ ?