The mass of the earth is $9$ times that of Mars. The radius of the earth is twice that of Mars. The escape velocity on earth is $12 k m / s e c$ . The escape velocity on Mars is ......... km/sec.

4 \sqrt{2}

km/sec

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2 \sqrt{2}

km/sec

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6 \sqrt{2}

km/sec

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8 \sqrt{2}

km/sec

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Solution

The correct option is D $4 \sqrt{2}$ km/sec
Escape speed is $v_{e} = \sqrt{\frac{2 G M}{R}} = 12$ km/s on Earth's surface.
Now, the mass of Mars is one-ninth and radius is half that of Earth's.
So,
$v_{m}^{^{'}} = \sqrt{\frac{2 G \times M / 9}{R / 2}} = \frac{\sqrt{2}}{3} \times \sqrt{\frac{2 G M}{R}} = \frac{\sqrt{2}}{3} \times 12 = 4 \sqrt{2}$ km/s

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The mass of the earth is 9 times that of Mars. The radius of the earth is twice that of Mars. The escape velocity on earth is 12km/sec. The escape velocity on Mars is ......... km/sec.

The correct option is D 4√2 km/secEscape speed is ve=√2GMR=12 km/s on Earth's surface.Now, the mass of Mars is one-ninth and radius is half that of Earth's.So,v′m=√2G×M/9R/2=√23×√2GMR=√23×12=4√2 km/s

The mass of the earth is $9$ times that of Mars. The radius of the earth is twice that of Mars. The escape velocity on earth is $12 k m / s e c$ . The escape velocity on Mars is ......... km/sec.