 Solution

ID: past-exam-of-the-physics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2016/paper-1/section-a/a5/solution

Far from its ends, approximate the body by an infinite uniform cylinder. By cylindrical symmetry, the Newtonian gravitational field is radial. Applying Gauss's law for gravity to a coaxial cylindrical surface of radius

s

ℓ

outside the material gives

g (s) 2 π s ℓ = 4 π Gρ π R^{2} ℓ, g (s) = \frac{2 π Gρ R ^{2}}{s} .

At the surface,

R = 50 m

, so

g (R) ≃ 2 π GρR ≃ 4.19 \times 1 0^{- 5} m s^{- 2} .

The gravitational acceleration points inward toward the axis. Its small magnitude reflects both the small size and the modest density. The infinite-cylinder approximation uses the specified distance from both ends; a spherical approximation would discard the relevant geometry. No rotational contribution is included, since no rotation rate is supplied.

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