The radii of two planets A and B are in the ratio 2 : 3. Their densities are 3$\rho$ and 5$\rho$ respectively. The ratio of their acceleration due to gravity is :
Solution
<p>Given,</p>
<p>${{{r_A}} \over {{r_B}}} = {2 \over 3}$</p>
<p>${{{\rho _A}} \over {{\rho _B}}} = {3 \over 5}$</p>
<p>We know,</p>
<p>Acceleration due to gravity</p>
<p>$$g = {{GM} \over {{r^2}}} = {G \over {{r^2}}} \times {4 \over 3}\pi {r^3} \times \rho $$</p>
<p>$= {{4\pi Gr\rho } \over 3}$</p>
<p>$\therefore$ $g \propto \rho r$</p>
<p>$\therefore$ $${{{g_A}} \over {{g_B}}} = {{{\rho _A}} \over {{\rho _B}}} \times {{{r_A}} \over {{r_B}}}$$</p>
<p>$= {3 \over 5} \times {2 \over 3}$</p>
<p>$= {2 \over 5}$</p>
About this question
Subject: Physics · Chapter: Gravitation · Topic: Gravitational Field and Potential
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