Question

The diameters of two plantes are in the ration 4:1 and their density in the ration 1:2 The acceleration due to gravity on the planets will be in ratio,

• A. 1 : 2
• B. 2 : 3
• C. 2 : 1
• D. 4 : 1

Answer 1

The correct option is C 2 : 1

$M_p=Density\times Volume=Density\times \frac{4\pi r^3}{3}$

$g=\frac{G{M}_p}{r^2}$

$g=\frac{G\times density\times 4\pi r^3}{3r^2}$

Thus $g\propto r$ and $g\propto Density$

So, $\frac{g_1}{g_2}=\frac{4\times 1}{1\times 2}=\frac{2}{1}$