# Problem: Suppose we could shrink the earth without changing its mass.  At what fraction of its current radius would the free-fall acceleration at the surface be three times its present value?

###### FREE Expert Solution

Weight is given by:

$\overline{){\mathbf{F}}{\mathbf{=}}{\mathbf{m}}{\mathbf{g}}}$, where g is the magnitude of gravitational acceleration on the surface of Earth

In full form, gravitational force is expressed as:

$\overline{){\mathbf{F}}{\mathbf{=}}\frac{\mathbf{G}\mathbf{M}\mathbf{m}}{{\mathbf{r}}^{\mathbf{2}}}}$

The gravitational force on an object is equal to its weight when the object is at the Earth's surface.

###### Problem Details

Suppose we could shrink the earth without changing its mass.  At what fraction of its current radius would the free-fall acceleration at the surface be three times its present value?