The linear mass density of a thin rod AB of length varies from A to B as

PHYSICS · Single correct · A Level · Physics · Engineering physics · Engineering physics

Problem

The linear mass density of a thin rod AB of length

L

varies from A to B as

\lambda(x) = \lambda_0 \left(1 + \frac{x}{L}\right)

, where

x

is the distance from A. If

M

is the mass of the rod then its moment of inertia about an axis passing through A and perpendicular to the rod is : (1)

\frac{5}{12} ML^2

(2)

\frac{7}{18} ML^2

(3)

\frac{2}{5} ML^2

(4)

\frac{3}{7} ML^2