Acceleration due to gravity question

AI Thread Summary
The discussion revolves around calculating the acceleration due to gravity on a planet with three times the mass and diameter of Earth. The formula used is g = GM/R^2, leading to the conclusion that the new gravitational acceleration g' should be greater than Earth's. However, the calculations suggest g' is less than g, which contradicts the expectation based on Newton's laws of gravity. The confusion arises from the relationship between mass and radius, as increasing diameter affects the gravitational force. Participants seek clarification on the correct approach to resolve this discrepancy.
srikar97
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Homework Statement



the mass of a planet is three times that of the Earth and the diameter of the planet is also three times that of the earth.what is the acceleration due to gravity on the surface of the planet.value of g on Earth's surface =9.80m/s^2

Homework Equations



g=GM/R^2

The Attempt at a Solution


g=GM/R^2

g'=GM'/R'^2

g'/g=(M'/M)(R^2/R'^2)

M'/M=3

R/R'=1/3, g=9.80 m/s^2

g/g'=3*1/9

g'=g/3=9.8/3=3.267 m/s^2[wrong answer]

but the Newton's laws of gravity say that mass is directly proportional to gravitational acceleration ,the mass of the planet is 3 times that of the Earth so g'>g but her
g'<g i don't know where i have gone wrong perhaps i have done some wrong calculations i am quite doubtful about the answer any help would be greatly appreciated
 
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I don't see anything wrong. What's the "correct" answer?
 
so am i correct? but i don't think it obeys Newton's laws of gravitation.. as it says more mass the more the gravitational acceleration on that planet...
 

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