If the radius of the earth shrinks by 2percent, mass remaining the same the how would the value of acceleration due to gravity change????

in percent

plz reply as soon as u can :):)

g= GM/R^2 ......(1) g=Acc. due to gravity , M- mass of the earth R-Radius of the Earth

Differentiating it, we have dg= -2GM/R^3 * dR ........(2)

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

Given radius of the earth shrinks by 2% ,

dR/R = -2/100

from (1) (2), % increase in the value of g is ----- dg/g *100 = -2dR/R *100

= -2 [ -2/100] *100

= 4%