A rod of length has non-uniform linear mass density given by

PHYSICS · Single correct · AP · Physics 1: Algebra-based · Force and Translational Dynamics · Force and Translational Dynamics

Problem

A rod of length

L

has non-uniform linear mass density given by

\rho(x) = a + b\left(\frac{x}{L}\right)^2

, where

a

and

b

are constants and

0 \le x \le L

. The value of

x

for the centre of mass of the rod is at: (1)

\frac{3}{2}\left(\frac{a+b}{2a+b}\right)L

(2)

\frac{3}{4}\left(\frac{2a+b}{3a+b}\right)L

(3)

\frac{4}{3}\left(\frac{a+b}{2a+3b}\right)L

(4)

\frac{3}{2}\left(\frac{2a+b}{3a+b}\right)L