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 10
24
kg and a radius of 6370 km. Ignore
rotation and assume that Earth is spherical. (a) Calculate g 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 g 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 g at a
depth of 25.0 km?
(Precise
measurements of g
are sensitive
probes of the
interior structure of
Earth, although
results can be
clouded by local
variations in mass
distribution.)

Explanation / Answer

b. 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 Compared to the gravitational acceleration at the surface, which is9.81 m/s² It makes sense that it went up because you are closer to the sourceof gravity.

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