Which of the four graphs correctly shows the dependence of gravitational acceleration g on distance r from the centre of a uniformly dense Earth of radius R?
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Question

Which of the four graphs correctly shows the dependence of gravitational acceleration g on distance r from the centre of a uniformly dense Earth of radius R?

G1 Physics · Accepted Answer

Step 1: Inside a uniformly dense sphere, enclosed mass M(r)∝r³ so g(r)=GM(r)/r²∝r. Step 2: Outside the sphere g(r)=GM/r², decreasing as 1/r². Thus the correct graph rises linearly to r=R and then decays as 1/r². Final answer: D — Image 4.