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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
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B
2 : 3
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C
2 : 1
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D
4 : 1
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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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