# If the radius of the earth shrinks by 2.5 % mass remaining constant. Then how would the value of acceleration due to gravity change?

Dear Student

g= GM/R2 ......(1)
g=Acc. due to gravity , M- mass of the earth R-Radius of the Earth

Differentiating it, we have dg= -2GM/R3 * dR ........(2)

Dividing (2) by (1) ,
dg/g = -2dR/R     .....(3)

Given radius of the earth shrinks by 2.5% ,

dR/R = -2.5/100

From (3)
% increase in the value of g is ----- dg/g *100 = -2dR/R *100

= -2 [ -2.5/100] *100

= 5%

So the value of acceleration due to gravity increases by 5%.
Regards

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