Please help with this easy Physics Homework
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Please help with this easy Physics Homework

[From: ] [author: ] [Date: 11-11-22] [Hit: ]
g = G(2M)/(2r)² = (1/2) x GM/r² = (1/2) x g = 9.8/2 = 4.9m/s²No calculation is necessary really.From the equation you can tell doubling M will increase g by a factor 2 and doubling rreduce g by 2² = 4 times. Overall effect is 2 x 1/4 = 1/2, i.......

I think your mistake was to forget to square the 3.
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C) If M becomes (2M) and r becomes (2r),
g' = G(2M)/(2r)² = (1/2) x GM/r² = (1/2) x g = 9.8/2 = 4.9m/s²

No calculation is necessary really. From the equation you can tell doubling M will increase g by a factor 2 and doubling r reduce g by 2² = 4 times. Overall effect is 2 x 1/4 = 1/2, i.e. g is halved.

I think you made the same mistake as in B)
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D) If r becomes (2r), g' = GM)/(2r)² = (1/4) x GM)/r² = (1/4) x g = 9.8/4 = 2.45m/s²

Again, it should be clear that doubling r reduces g by 2² = 4 times.

There is no difference between moving to a distance of 2r and expanding the earth to double its radius (keeping M constant). This is because, providing we are at the surface or outside the surface, the Earth's gravitational field behaves the same as a point mass, M, located at the earth's centre. We can use g = -GM/r² just as if there was a point mass M and we wanted g at some distance, r, from it.

(However if we are inside the earth, this is no longer true - the field inside the earth drops from g at the surface to zero at the centre! - we can't use GM/r² inside the earth, only at the surface and outside.)
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