Question

A rocket has landed on Planet X, which has half the radius of Earth. An astronaut onboard the rocket weighs twice as much on Planet X as on Earth. If the escape velocity for the rocket taking off from Earth is v0 , then its escape velocity on Planet X is:

Answer 1

Explanation:

Let acceleration due to Gravity for a planet is given by:

$g_X=GM/R^2$

Here,$g_X = 2g$

Escape velocity is given by:

$v =\sqrt{ \frac{2GM} {R}} = \sqrt{2aR}$

Here, $R=R_earth/2$

and g_X = 2g

Therefore,$v=\sqrt(2(2g)(R/2))=v_0$

Answer 2

The escape velocity for both the planets is the$v_0$

• The calculation is as follows:

Acceleration due to Gravity for a planet is provided by

$a = GM\div R^2$

Here, a = 2g

Escape velocity is provided by:

$v = \sqrt{\frac{2GM}{R} } = \sqrt{2aR}$

Here, R = REarth/2 and a = 2g

So,

$v = \sqrt{2(2g)(R\div 2)} = v_0$

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