Figure 13-32 shows, not to scale, a cross section through the interior of Earth. Rather than being uniform throughout, Earth is divided into three zones: an outer crust, a mantle, and an inner core. The dimensions of these zones and the masses contained within them are shown on the figure. Earth has a total mass of \( 5.98 \times 10^{24} \mathrm{~kg} \) and a radius of \( 6370 \mathrm{~km} \). Ignore rotation and assume that Earth is spherical.
Suppose that Earth were a uniform sphere with the same total mass and size. What would be the value of \( a_{\mathrm{g}} \) at a depth of \( 25.0 \mathrm{~km} \) ? (Precise measurements of \( a_{\mathrm{g}} \) are sensitive probes of the interior structure of Earth, although results can be clouded by local variations in mass distribution.)
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