Question

# Two planet have radii in the ratio $$1:2$$ and densities in the ratio $$1:3$$. The value of the ratio between acceleration due to gravity on the first planet to that of the second planet is:

A
6
B
3
C
1/4
D
1/6

Solution

## The correct option is D $$1/6$$$$g=\dfrac{GM_p}{r^2}$$$$M_p=Density\times Volume=Density\times\dfrac{4\pi r^3}{3}$$$$g=\dfrac{G\times density\times 4\pi r^3}{3r^2}$$Thus g$$\propto r$$ and g$$\propto Density$$So,$$\dfrac{g_1}{g_2}=\dfrac{1\times 1}{2\times 3}=\dfrac{1}{6}$$ Physics

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