**1. The problem statement, all variables and given/known data**

A uniform sphere has mass M and radius r. A spherical cavity (no mass) of radius r/2 is then carved within this sphere (the cavity’s surface passes through the sphere’s center and just touches the sphere’s outer surface). The centers of the original sphere and the cavity lie on a straight line, which defines the x axis.

With what gravitational force will the hollowed-out sphere attract a point mass m which lies on the x axis a distance d from the sphere’s center? [Hint: Subtract the effect of the "small" sphere (the cavity) from that of the larger entire sphere.]

**2. Relevant equations**

[itex] F = G\frac{m_1m_2}{r^2} [/itex]

**3. The attempt at a solution**

Let mass [itex] M_f [/itex] = the mass of the sphere without the cavity, [itex] M_c [/itex] = the mass of the cavity, and [itex] R_f [/itex] = the distance between the two masses.

[itex] M_f = M – M_c [/itex]

[itex] R_f = d + R_2 [/itex]

[itex] F = G\frac{(M_f) m}{(R_f)^2} [/itex]

is this right?

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