Question

Suppose that the earth retained is present mass but was somehow compressed to half its present radius. What would be the value of g , the accelaration due to gravity, at the surface of this new, compact planet ?

Answer 1

We know, $g=\frac{GM}{R^2}$

therefore $g\propto \frac{1}{R^2}$

So when radius is reduced to half then the value of $g$ will increase 4 times

$g^{\prime }=4\times g=4\times 9.8=39.2m/s^2$