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Gravitation Part 2

Section: Physics

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Question : 54 of 110

Marks: +1, -0

The ratio of escape velocity of a planet to the escape velocity of earth will be :-

Given : Mass of the planet is 16 times mass of earth and radius of the planet is 4 times the radius of earth.

[12-Apr-2023 shift 1]

$1:4$
$4:1$
$2:1$
$1:\sqrt{2}$

Solution:

Given mass of planet

=16

mass of the earth

(m_p = 16 m_e)

r_p = 4 r_{\text{o}}

We know

V_{\text{escape}} = \sqrt{\frac{2 G m}{R}}, \frac{V_{\text{esplanet}}}{V_{\text{esearth}}} =

?

\frac{V_{\text{es plavet}}}{V_{\text{es earth}}} = \sqrt{\frac{2 GM_p}{R_p} \times \frac{R_e}{2 GM_e}}

= \sqrt{\frac{M_p}{M_e} \times \frac{R_e}{R_p}}

= \sqrt{\frac{16 m_e}{m_e} \times \frac{R_e}{4 R_e}}

= \sqrt{\frac{16}{4}} = 2:1

\frac{V_{\text{esplanet}}}{V_{\text{eseath}}} = \frac{2}{1}

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