A straight rod extends from x = α to x = α + ℓ. Its linear mass density is μ(x) = a + bx². Find the gravitational force exerted by the rod on a point mass m at x = 0.

Question

G1 Physics · Accepted Answer

A rod element dx at coordinate x has mass dm = (a+bx²)dx. Its gravitational force on m is dF = Gm dm/x² = Gm(a/x² + b)dx toward +x. Integrating from α to α+ℓ givₑ F = Gm[a(1/α - 1/(α+ℓ)) + bℓ]. Correct answer: A.