Question

Suppose the earth shrinks such that its radius decreases to half the present value. What will be the acceleration due to gravity on the surface of the earth?

Answer 1

Acceleration due to gravity

$g=\frac{GM}{R^2}$

When radius reduces to half then

$g^{\prime }=\frac{GM}{{\left(R/2\right)}^2}$

$g^{\prime }=\frac{4GM}{R^2}$

$g^{\prime }=4\times 9.8$

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

If radius reduces to half, then acceleration due to gravity will become four times.