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If the distance between earth and sun is increased by 2% then find the percentage change in gravitational force acting between them ?

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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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