physics gravitation(radius of earth ) help. needed please

Question

If the radius of the earth shrinks by 1.5 % (mass remaining the same ) , then the value of acceleration due to gravity changes by ?

1.   1%
2.   2%
3.   3%
4.   4%

Answer 1

Gravitational force goes as 1/R².

 

Original Force goes as (1/R₁)²

 

Final force goes as (1/R₂)²

 

Problem specifies that:

 

R₂=0.985R₁

 

Ratio of final force to initial force is:

 

[(1/R₂)²]/[(1/R₁)²]=0.985²=0.970

 

3% is the correct answer.