Question

if the radius of the earth were to shrink by one percent, its mass remaining the same, the acceleration due to gravity on the earth's surface would:

Answer 1

http://en.wikipedia.org/wiki/Gravity_of_Earth#Estimating_g_from_the_law_of_universal_gravitation

\[g = G \frac{M}{r^2}\]
plug in .99r for radius since it shrinks by 1%
\[g_1 = G \frac{M}{(.99r)^2} = 1.0203 G \frac{M}{r^2} = 1.0203 g\]
Thus acceleration due to gravity would increase by about 2%