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Escape Speed

The escape ve...

Question

The escape velocities on two planets of masses $m_{1}$ and $m_{2}$ , having same radius, are $v_{1}$ and $v_{2}$ respectively, then

A

\frac{v_{1}}{v_{2}} = \frac{m_{1}}{m_{2}}

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B

\frac{v_{2}}{v_{1}} = \frac{m_{1}}{m_{2}}

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C

\frac{v_{1}}{v_{2}} = {(\frac{m_{1}}{m_{2}})}^{2}

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D

\frac{v_{1}}{v_{2}} = \sqrt{\frac{m_{1}}{m_{2}}}

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Solution

The correct option is D $\frac{v_{1}}{v_{2}} = \sqrt{\frac{m_{1}}{m_{2}}}$
$v_{e} = \sqrt{2 G M / R}$
Thus,
$v_{1} / v_{2} = \sqrt{m_{1} / m_{2}}$

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