If the radius of the Earth shrinks by `2%`, mass remaing same, then how would the have of acceleration due to gravity change?

If the radius of the Earth shrinks by `2%`, mass remaing same, then ho

1.	If the radius of the Earth shrinks by `2%`, mass remaing same, then how would the have of acceleration due to gravity change?
Answer» Let `M,R` be tha mass and redius of the Earth. The acceleration due to gravity on the surface of Earth is given by `g = GM//R^(2)` ..(i) Differentiating it, we have, `dg = - (2GM)/(R^(3))dR` ..(ii) Dividing (iii) by (i), we have, `(dg)/(g) = - (2dR)/(R )` ..(iii) When redius of earth shrinks by `2%` then, `(dR)/(R ) = - (2)/(100)` ..(iv) From (iii) & (iv), the `%` increase in the value of `g` is `= (dg)/(g) xx 100 = - (2dR)/(R ) xx 100 = - [(-2)/(100)] xx 100` `= 4 %`

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If the radius of the Earth shrinks by `2%`, mass remaing same, then how would the have of acceleration due to gravity change?

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