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Question

The escape velocity of an object on a planet whose radius is 4 times that of the earth and $$g$$ value 9 times that on the earth, in kms$$^{-1}$$ is


A
33.6
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B
67.2
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C
16.8
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D
25.2
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Solution

The correct option is B 67.2
Escape speed is given by, $$v_{min}=\sqrt {2gR}$$
which is equal to $$\approx11.2$$ km/s on Earth's surface.
For another planet with radius 4 times and $$g$$ value 9 times that of Earth
$$v^{'}_{min}=\sqrt {2\times9g\times4R}$$
        $$=6 \times \sqrt {2gR}=6\times11.2$$
        $$=67.2$$ $$km/s$$

Physics

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