If the radius of the earth shrinks by 2 5 % mass remaining constant Then how would the value - Physics - Work Energy And Power

Question

If the radius of the earth shrinks by 2 5 % mass remaining constant
Then how would the value of acceleration due to gravity change?

Vipra Mishra · Accepted Answer

Dear Student
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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

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