The figure shows, not to scale, a cross section through the interior of Earth. R

Question

The figure 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 x 1024 kg and a radius of 6370 km. Ignore rotation and assume that Earth is spherical. (a) Calculate ag at the surface. (b) Suppose that a bore hole (the Mohole) is driven to the crust–mantle interface at a depth of 25.0 km; what would be the value of ag at the bottom of the hole? (c) Suppose that Earth were a uniform sphere with the same total mass and size. What would be the value of ag at a depth of 25.0 km? (Precise measurements of ag are sensitive probes of the interior structure of Earth, although results can be clouded by local variations in mass distribution.)

Explanation / Answer

(a)

ag= GM/r^2
G is the gravitational constant, 6.673 x 10^-11
M is the mass of the planet
r is the radius

since we go down 60 km, we do 6,370-60= 6,310 km
Im going to turn it into meters
6.673 x 10^-11 x 5.98 x 10^24/6,310,000^2
ag= 10.02 m/s²

(b)
Compared to the gravitational acceleration at the surface, which is 9.81 m/s²
It makes sense that it went up because you are closer to the source of gravity.

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