Question Detail
Question
What is the moment of inertia of a thin rod of mass M and length L about an axis perpendicular to the rod and passing through one of its ends?
Correct Answer
Option B is the correct answer.
Detailed Explanation
The moment of inertia is calculated by integrating x² dm from 0 to L. With dm = (M/L) dx, the integral ∫₀ᴸ x² (M/L) dx evaluates to (1/3) M L². This is the standard formula for a rod about its end.
Hint
Consider the integral I = ∫ r² dm, where r is the distance from the axis to a mass element dm along the rod.