If the escape velocity on earth is $11.2 k m / s e c$ , its value for a planet having double the radius and $8$ times the mass of earth is ..... $m / s e c$ .

11.2 km/sec

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22.4 km/sec

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5.6 km/sec0

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8 km/sec

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Solution

The correct option is A 22.4 km/sec
Escape speed, $v_{e} = \sqrt{\frac{2 G M}{R}} = 11.2$ $k m / s$
For another planet mass is 8 times and radius is twice that of Earth.
$∴ v_{e}^{^{'}} = \sqrt{\frac{2 G \times 8 M}{2 R}}$
$\Rightarrow v_{e}^{^{'}} = 2 \sqrt{\frac{2 G M}{R}} = 2 \times 11.2 = 22.4$ km/s

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If the escape velocity on earth is 11.2km/sec, its value for a planet having double the radius and 8 times the mass of earth is ..... m/sec.

The correct option is A 22.4 km/secEscape speed, ve=√2GMR=11.2 km/sFor another planet mass is 8 times and radius is twice that of Earth.∴v′e=√2G×8M2R⇒v′e=2√2GMR=2×11.2=22.4 km/s

If the escape velocity on earth is $11.2 k m / s e c$ , its value for a planet having double the radius and $8$ times the mass of earth is ..... $m / s e c$ .