If the distance between earth and sun is increased by 2% then find the percentage change in gravitational force acting between them ?
Answer
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Distance between sun and earth= r
mass of earth= m
mass of sun= M
Force of attraction = F= GmM/r²
r' = r + 0.02r
r'= 102/100r
F'= GmM/r'²
F'/F= GmM/r'² / GmM/r² = (r/r' )²
= 100/102)²
1-F'/F = 1- (100/102)²
decrease in F= 1- 0.96
= 0.039 or 3.96%
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