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Question

Imagine a new planet having the same density as that of earth but it is 3 times bigger than the earth in size. If the acceleration due to gravity on the surface of earth is g and that on the surface of the new planet is g' then that would be the relation between them ?

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Solution

If the mass and radius of the new planet be M and R,
then for same density as earth,
R=3R & M=27M [MαV, where VαR3]
Now for Earth,
g=GMR2(1)
and for new planet,
g=GMR2=G(27M)(3R)2=3(GMR2)=3g.

1104363_1179405_ans_028b09475d924987b183068504cddc34.JPG

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