Question

If the radius of the earth is reduced to half of its present value, with no change in the mass, how will the acceleration due to gravity, be affected?

Answer 1

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

If $R\to \frac{R}{2}$

$4M\to M$

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

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