Question

if the Earth shrinks, what will happen to acceleration due to gravity?

Answer 1

If the Earth shrinks, the radius due to gravity will increase drastically. This is because, acceleration due to gravity is indirectly proportional to radius of the Earth. (g=GM÷r²).  

MORE==> What Will Happen to Accelaration due to Gravity If Earth's Radius Shrinks by 1% Let the mass and radius of the earth be M and R respectively.

Acceleration due to gravity, g = GM/R^2

When the radius, R’ = R-R/100 = 99R/100 = 0.99R

So, the acceleration due to gravity, g’ = GM/(0.99R)^2

or, g’ = 1.02GM/R^2

Now, the change in acceleration due to gravity,

=g’ – g

=(1.02-1)GM/R^2

= (0.02)GM/R^2

Thus, the acceleration due to gravity increases by 2%.