Answer
$37.87$
Work Step by Step
Step 1. On the Moon, $W=a+\frac{b}{g_m}$, $dW_m=-\frac{b}{g_m^2}dg=-\frac{b}{5.2^2}dg$
Step 2. On the Earth, $W=a+\frac{b}{g_e}$, $dW_e=-\frac{b}{g_e^2}dg=-\frac{b}{32^2}dg$
Step 3. The ratio: $\frac{dW_m}{dW_e}=\frac{-\frac{b}{5.2^2}dg}{-\frac{b}{32^2}dg}=(\frac{32}{5.2})^2\approx37.87$. It seems that the work change is more sensitive to the gravity change on the Moon than on the Earth.
