Question

A thin rod lies along the $x$-axis from $x=0$ to $x=0.60cm$. The linear density of the rod, $\lambda$, is given by the equation: $\lambda =2.0-3.0x$ and is in units of $kg/m$.
Where is the Center of Mass of the rod?

• A. At $x=0.14m$
• B. At $x=0.20m$
• C. At $x=0.22m$
• D. At $x=0.30m$
• E. At $x=0.38m$

Answer 1

The correct option is A At $x=0.14m$

The center of mass of the rod from $x=0$ is given by

$x_{CM}={\int }_0^{x_0}x\left(\lambda dx\right)$

$={\int }_0^{x_0}(2x-3x^2)dx$

$=0.14m$