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Question

If the radius of the earth shrinks by 4% and there is no change in its mass then by how much does the value of g change?
( Given for x<<1 , assume 1(1−x)2≈1+2x)

A
2%
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B
8%
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C
4%
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D
16%
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Solution

The correct option is B 8%
Let Me be the mass of earth.
Let R1 be the initial radius of the earth.

Acceleration due to gravity g1=GMeR12

Radius shrinks by 4%, and there's no change in mass.

R2=R1×(14100)
R2=96100×R1

Now, acceleration due to gravity: g2=GMeR22
=GMe(14100)2(R1)2
GMe(R1)2×(1+2×4100)
=g1×(1+8100)

Thus, the value of g changes by 8%.

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