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Understanding of Field

A planet in a...

Question

A planet in a distant solar system is 10 times more massive than the earth and its radius 10 times smaller. If the escape velocity from the surface of earth is 11 km/sec, the escape velocity from the surface of the planet would be

A

1.1 km/sec

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B

11 km/sec

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C

110 km/sec

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D

0.11 km/sec

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Solution

The correct option is C 110 km/sec
$v_{e} = \sqrt{\frac{2 G M_{e}}{R_{e}}} v_{p} = \sqrt{\frac{2 G M_{p}}{R_{p}}} ∴ \frac{v_{p}}{v_{e}} = \sqrt{\frac{M_{p}}{M_{e}} . \frac{R_{e}}{R_{p}}} = \sqrt{10 \times 10} ∴ v_{p} = 10. v_{e}$

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