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  • 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 ear

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.

Option: 1

1:4


Option: 2

4:1


Option: 3

2:1


Option: 4

1:\sqrt{2}


Answers (1)

best_answer

Given mass of planet = 16 mass of the earth (mp = 16 me)
r_p=4 r_e

\begin{aligned} & \text { We know } \mathrm{V}_{\text {escape }}=\sqrt{\frac{2 \mathrm{Gm}}{\mathrm{R}}}, \frac{\mathrm{V}_{\text {esplanet }}}{\mathrm{V}_{\text {esearth }}}=\text { ? } \\ & \frac{V_{\text {es planet }}}{\mathrm{V}_{\text {es earth }}}=\sqrt{\frac{2 \mathrm{GM}_{\mathrm{p}}}{\mathrm{R}_{\mathrm{p}}} \times \frac{\mathrm{R}_{\mathrm{e}}}{2 \mathrm{GM}_{\mathrm{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 \\ & \end{aligned}



\frac{\mathrm{V}_{\text {esplanet }}}{\mathrm{V}_{\text {esearth }}}=\frac{2}{1}

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Rishi

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