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If earth has mass nine times and radius twice that of the planet mars, calculate the velocity required by a rocket to pull out of the gravitational force of mars. $(V_{e} = 11.2 K m / s)$

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a

7.92 Km/s

b

5.3 Km/s

c

9.6 Km/s

d

2.53 Km/s

answer is C.

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Detailed Solution

$V_{e} = \sqrt{\frac{2 G m}{R}} \frac{V_{M}}{V_{E}} = \sqrt{\frac{2 G M_{M}}{R_{M}} \times \frac{R_{E}}{2 G M_{E}}} = \sqrt{\frac{M_{M} \times R_{M} \times 2}{R_{M} \times 9 M_{M}}} = \frac{\sqrt{2}}{3} V_{M} = \frac{1.414}{3} \times 11.2 = 5.3 K m / s$

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