Gravitation Question 331

Question: If the radius of the earth were to shrink by 1 %, with its mass remaining the same, the acceleration due to gravity on the earth’s surface would

Options:

A) Decrease by 1%

B) decrease by 2%

C) Increase by 1%

D) increase by 2%

Show Answer

Answer:

Correct Answer: D

Solution:

  • As $ [g=\frac{GM}{R^{2}}] $

    when radius is reduced by 1% then $ [R’=R-\frac{R}{100}=.99R,] $

    so $ [g’=\frac{GM}{{{(.99R)}^{2}}}=1.02\frac{GM}{R^{2}}] $

    %$ [\Rightarrow increase=2] $ %



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