A rod length `L` and mass `M` is placed along the `x`-axis with one end at the origin, as shown in the figure above. The rod has linear mass density `lamda=(2M)/(L^(2))x,` where `x` is the distance from the origin. Which of the following gives the `x`-coordinate of the rod's center of mass?

Options

A. `2/3L`
B. `1/4L`
C. `1/3L`
D. `1/2L`

Answer

A

Explanation

`X_(cm)=1/M int x dm=1/M int_(0)^(L) x((2m)/(L^(2))x)dx=(2L)/3`