Physics

Problem

A thin rod of length

L

has a linear mass density that varies with distance

x

from one end according to

\lambda(x)=\lambda_0 x

. a. (i) Obtain an expression for the total mass

M

of the rod in terms of

\lambda_0

and

L

. b. (ii) Hence derive an expression for its moment of inertia about the end

x=0

in terms of

M

and

L