Physics

Problem

A non-uniform rod of total length

2L

has linear mass density

\lambda(x)=\lambda_0\Bigl(1+\dfrac{x^{2}}{L^{2}}\Bigr)

, where

x

is the distance measured from the centre of the rod (origin at the centre,

-L\le x\le L

). Determine the moment of inertia of the rod about an axis through its centre and perpendicular to its length, expressed in terms of its total mass

M

and

L

. a)

\dfrac{1}{2}ML^{2}

\dfrac{1}{3}ML^{2}

\dfrac{2}{5}ML^{2}

\dfrac{3}{5}ML^{2}