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

Solution

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

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