The moment of inertia of a uniform cylinder of length l and radius R about its perpendicular bisector is I. What is the ratio l/R such that the moment of inertia is minimum ?
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The moment of inertia of a uniform cylinder of length l and radius R about its perpendicular bisector is I. What is the ratio l/R such that the moment of inertia is minimum ?

G1 Physics · Accepted Answer

For a uniform cylinder of fixed mass and density, volume πR²ℓ is constant, so ℓR²=constant. About the perpendicular bisector, I=M(3R²+ℓ²)/12. Eliminating ℓ using the volume constraint and minimizing gives ℓ²=(3/2)R². Hence ℓ/R=√(3/2), option C.