If the radius of the earth decreases by 1% without changing its mass, will the acceleration due to gravity at the surface of the earth increase or decrease? If so, by what percent?

If the radius of the earth decreases by 1% without changing its mass,

1.	If the radius of the earth decreases by 1% without changing its mass, will the acceleration due to gravity at the surface of the earth increase or decrease? If so, by what percent?
Answer» We know that, `g = (GM)/(R^(2))` or `g prop (1)/(R^(2))` So `(g_(2))/(g_(1)) = ((R_(1))/(R_(2)))^(2)` If `R_(1) = R`, then `R_(2) = R +- n% R = (1 +- n%)R` `:. (g_(2))/(g_(1)) = [(R)/((1 +- n%)R)]^(2) = (1)/((1 +- n%)^(2))` `= (1 +- n%)^(-2)` `%` increase or decrease in the value of `g` is `= ((g_(2) - g_(1))/(g_(1))) xx 100 = ((g_(2))/(g_(1)) - 1) xx 100` `= [(1 +- n%)^(-2) - 1] xx 100`

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If the radius of the earth decreases by 1% without changing its mass, will the acceleration due to gravity at the surface of the earth increase or decrease? If so, by what percent?

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