Question

Moment of inertia of a cylinder of mass M, length L and radius R about an axis passing through its centre and perpendicular to the axis of the cylinder is I = M \(=M(\frac{R^2}{4} + \frac{L^2}{12})\). If such a cylinder is to be made for a given mass of a material, the ratio L/R for it to have minimum possible I is

(1) \(\sqrt\frac{2}{3}\)

(2) \(\frac{2}{3}\)

(3) \(\frac{3}{2}\)

(4) \(\sqrt\frac{3}{2}\)

Answer 1

 (4) \(\sqrt\frac{3}{2}\)

\(I=M(\frac{R^2}{4} + \frac{L^2}{12})\)