Free Version
Easy

# Center of Uneven Density Rod

MVCALC-LNJKYJ

Assume a thin rod $L$ lies between $0$ and $2$ has density given by:

$$$$\rho(x)= \begin{cases} x^3, \quad \forall x\in[0,1] \\\ 2x-x^2, \quad \forall x\in (1,2] \end{cases}$$$$

Find the center of mass for $L$.

A

$\cfrac{67}{60}$

B

$\cfrac{67}{55}$

C

$\cfrac{11}{12}$

D

$\cfrac{37}{21}$

E

$\cfrac{12}{11}$