A planet having mass and radius , where and are mass and radius of Earth respectively, has escape velocity in km/s given by: (Given escape velocity on Earth ) [2023]

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Solution

Q.
A planet having mass $9 M_{e}$ and radius $4 R_{e}$ , where $M_{e}$ and $R_{e}$ are mass and radius of Earth respectively, has escape velocity in km/s given by: (Given escape velocity on Earth $V_{e} = 11.2 \times 10^{3} m/s$ ) [2023]

1 67.2

2 16.8

3 33.6

4 11.2

Ans.
(2)

$V_{P} = \sqrt{\frac{2 G M_{P}}{R_{P}}}, V_{E} = \sqrt{\frac{2 G M_{E}}{R_{E}}}$

$\frac{V_{P}}{V_{E}} = \frac{\sqrt{\frac{2 G M_{P}}{R_{P}}}}{\sqrt{\frac{2 G M_{E}}{R_{E}}}} = \sqrt{\frac{R_{E}}{R_{P}} \times \frac{M_{P}}{M_{E}}}$

$V_{P} = \sqrt{\frac{1}{4} \times 9} \times V_{E} = \frac{3}{2} V_{E}$

$V_{P} = \frac{3}{2} \times 11.2 km/sec = 16.8 km/sec$

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