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
4%
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C
16%
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D
8%
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Solution
The correct option is D8% 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×(1−4100) ⇒R2=96100×R1
Now, acceleration due to gravity: g2=GMeR22 =GMe(1−4100)2(R1)2 ≈GMe(R1)2×(1+2×4100) =g1×(1+8100)