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  • The escape velocities of two planets A and B are in the ratio 1: 2. If the ratio of their radii respectively is 1: 3, then the ratio of acceleration due to gravity of planet A to the acceleration o

The escape velocities of two planets A and B are in the ratio 1: 2. If the ratio of their radii respectively is 1: 3, then the ratio of acceleration due to gravity of planet A to the acceleration of gravity of planet B will be :

Option: 1

\frac{3}{2}


Option: 2

\frac{2}{3}


Option: 3

\frac{3}{4}


Option: 4

\frac{4}{3}


Answers (1)

best_answer

Given 

\begin{aligned} & \frac{\mathrm{v}_{\mathrm{A}}}{\mathrm{v}_{\mathrm{B}}}=\frac{1}{2} \\ & \frac{\mathrm{r}_{\mathrm{A}}}{\mathrm{r}_{\mathrm{B}}}=\frac{1}{3} \\ & \frac{\mathrm{g}_{\mathrm{A}}}{\mathrm{g}_{\mathrm{B}}}=? \end{aligned}

As we know,

\mathrm{v}=\sqrt{\frac{2 \mathrm{GM}}{\mathrm{R}}}

Hence,

\frac{\mathrm{v}_{\mathrm{A}}}{\mathrm{v}_{\mathrm{B}}}=\frac{\sqrt{\frac{2 \mathrm{GM}_{\mathrm{A}}}{\mathrm{R}_{\mathrm{A}}}}}{\sqrt{\frac{2 \mathrm{GM}_{\mathrm{B}}}{\mathrm{R}_{\mathrm{B}}}}}=\sqrt{\frac{\mathrm{M}_{\mathrm{A}} \mathrm{R}_{\mathrm{B}}}{\mathrm{M}_{\mathrm{B}} \mathrm{R}_{\mathrm{A}}}}=\frac{1}{2} _____________(i)

Given

\frac{\mathrm{R}_{\mathrm{A}}}{\mathrm{R}_{\mathrm{B}}}=\frac{1}{3}:__________(ii)

Therefore,

\begin{aligned} \frac{g_{\mathrm{A}}}{g_{\mathrm{B}}} & =\frac{\mathrm{M}_{\mathrm{A}} \mathrm{R}_{\mathrm{A}}^2}{\mathrm{M}_{\mathrm{B}} \mathrm{R}_{\mathrm{B}}^2} \\ & =\frac{1}{4} \times \frac{1}{3} \times 9 \\ & =\frac{3}{4} \end{aligned}

Posted by

jitender.kumar

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