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Question

My question is that when the density of a planet is equal to the density of Earth but twice its radius why it's acceleration due to gravity becomes less than that of Earth, why doesn't it becomes greater

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Solution

g=GMm/r^2
here GM is constant

Density=mass/volume
so mass=density×volume
volume of sphere=4/3×pie×r^3
substitute this for mass
mass(m)=density×(4/3)×pie×r^3
so g=GM×density×(4/3)×pie×r^3/r^2
so here r^2 in denominator cancels and g= a constant×r
so the g decreases
constant=GM×density×4/3×pie

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