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A narrow hole is drilled through the centre of earth (mass M kg and radius R m).
Now consider a particle of mass m which is inside the hole at a distance r m from
the centre.
(a) Show that
p3
M, = M-
R3
where M, is the mass of a smaller sphere with radius r inside the earth.
Hint: Assume the earth is a uniform sphere and that its density is the same every-
where.

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