(a) Consider two point masses, each having mass m, that are separated vertically by a distance of 1 cm just above the surface of a neutron star of radius R and mass M. Using Newton's law of gravity (Eq. 2.11), find an expression for the ratio of the gravitational force on the lower mass to that on the upper mass, and evaluate this expression for R=10 km, M=1.4M⊙, and m=1 g.
(b) An iron cube 1 cm on each side is held just above the surface of the neutron star described in part (a). The density of iron is 7860kgm−3. If iron experiences a stress (force per cross-sectional area) of 4.2×107Nm−2, it will be permanently stretched; if the stress reaches 1.5×108Nm−2, the iron will rupture. What will happen to the iron cube? (Hint: Imagine concentrating half of the cube's mass on each of its top and bottom surfaces.) What would happen to an iron meteoroid falling toward the surface of a neutron star?