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

at R/

Explanation:

The free-fall acceleration at the surface of Earth is given by

where

G is the gravitational constant

M is the Earth's mass

R is the Earth's radius

The formula can be rewritten as

(1)

We want to shrink the Earth at a radius R' such that the acceleration of gravity becomes 3 times the present value, so

g' = 3g

Keeping the mass constant, M, and substituting into the equation, we have