Moment of inertia of a cylinder of mass

MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

M

, length

L

and radius

R

about an axis passing through its centre and perpendicular to the axis of the cylinder is

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

. 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)

\frac{2}{3}

(2)

\frac{3}{2}

(3)

\sqrt{\frac{3}{2}}

(4)

\sqrt{\frac{2}{3}}