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.

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?

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What scientific concept do you need to know in order to solve this problem?

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