Planet A has mass M and radius R. Planet B has half the mass and half the radius of Planet A. If the escape velocities from the Planets A and B are vA and vB, respectively, then ${{{v_A}} \over {{v_B}}} = {n \over 4}$. The value of n is :
Solution
Escape velocity, V<sub>e</sub> = $\sqrt {{{2GM} \over R}}$
<br><br>V<sub>A</sub> = $\sqrt {{{2GM} \over R}}$
<br><br>V<sub>B</sub> = $\sqrt {{{2G{M \over 2}} \over {{R \over 2}}}}$ = $\sqrt {{{2GM} \over R}}$
<br><br>${{{V_A}} \over {{V_B}}}$ = 1
<br><br>Given ${{{V_A}} \over {{V_B}}} = {n \over 4}$
<br><br>$\therefore$ ${n \over 4}$ = 1
<br><br>$\Rightarrow$ n = 4
About this question
Subject: Physics · Chapter: Gravitation · Topic: Kepler's Laws
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