A thin rod of length L has a mass/length ratio proportional to x-the distance measured from end A. The moment of inertia of the rod about an axis passing through A, perpendicular to the rod, is A) proportional to x. B) proportional to x². C) proportional to x³. D) proportional to x⁴.

Question

Quizplus · Accepted Answer

The mass/length ratio is proportional to x, so the mass element dm is proportional to x dx. The moment of inertia dI for a small element is x^2 dm, which becomes proportional to x^3 dx. Integrating over the length of the rod gives a moment of inertia proportional to x^3.

A Thin Rod of Length L Has a Mass/length Ratio