The escape velocity for Earth is . A planet having 9 times mass of Earth and radius, 16 times that of Earth, has the escape velocity of [2024]

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Solution

Q.
The escape velocity for Earth is $v$ . A planet having 9 times mass of Earth and radius, 16 times that of Earth, has the escape velocity of [2024]

1 $\frac{v}{3}$

2 $\frac{2 v}{3}$

3 $\frac{3 v}{4}$

4 $\frac{9 v}{4}$

Ans.
(3)

The escape velocity of Earth,

$v = \sqrt{\frac{2 G M_{e}}{R_{e}}} = \sqrt{\frac{2 G \times 9 M_{e}}{16 R_{e}}}$ $(∵ \begin{matrix} M_{p} = 9 M_{e} \\ R_{p} = 16 R_{e} \end{matrix})$

$= \frac{3}{4} \sqrt{\frac{2 G M_{e}}{R_{e}}} \Rightarrow v_{p} = \frac{3}{4} v$ (using above eqn.)

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