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Two planets have the same average density but their radii are $R_1$ and $R_2$. If acceleration due to gravity on these planets be $g_1$ and $g_2$ respectively, then
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Verified Answer
The correct answer is:
$\frac{g_1}{g_2}=\frac{R_1}{R_2}$
According to Gravitational law
\(F=\frac{G M, M_2}{r^2}\) ...(i)
Where \(m_1 \rightarrow\) mass of planet
\(m_2 \rightarrow\) mass of any body
Now, According to Newton's second law, a body of Mass \(m_2\) fuels gravitational acceleration ' \(g\) ' which is
\(F=M_2 g\) ...(ii)
So, from (i) & (ii) we get,
\(g=\frac{G M_1}{\gamma^2}\)
So, the ratio of gravitational acceleration due to two planet is
\(\begin{aligned}
& \frac{g_1}{g_2}=\frac{m_1}{r_1^2} \times \frac{r_2^2}{m_2}=\frac{(4 / 3) \pi r_1^3 \times \rho}{r_1^2} \times \frac{r_2^2}{(4 / 3) \pi r_2^3 \times \rho} \\
& \therefore \frac{g_1}{g_2}=\frac{r_1}{r_2} \\
& \text {Answer:- } \frac{g_1}{g_2}=\frac{r_1}{r_2}
\end{aligned}\)
\(F=\frac{G M, M_2}{r^2}\) ...(i)
Where \(m_1 \rightarrow\) mass of planet
\(m_2 \rightarrow\) mass of any body
Now, According to Newton's second law, a body of Mass \(m_2\) fuels gravitational acceleration ' \(g\) ' which is
\(F=M_2 g\) ...(ii)
So, from (i) & (ii) we get,
\(g=\frac{G M_1}{\gamma^2}\)
So, the ratio of gravitational acceleration due to two planet is
\(\begin{aligned}
& \frac{g_1}{g_2}=\frac{m_1}{r_1^2} \times \frac{r_2^2}{m_2}=\frac{(4 / 3) \pi r_1^3 \times \rho}{r_1^2} \times \frac{r_2^2}{(4 / 3) \pi r_2^3 \times \rho} \\
& \therefore \frac{g_1}{g_2}=\frac{r_1}{r_2} \\
& \text {Answer:- } \frac{g_1}{g_2}=\frac{r_1}{r_2}
\end{aligned}\)
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