Question

A rod of length $4m$ is placed along x-axis. The rod is non-uniform and the mass per unit length of rod varies as $\lambda =x^2-4x+4$


then center of mass of rod is at

• A. $x=2m$
• B. $x=3m$
• C. $x=1m$
• D. $x=1.5m$

Answer 1

The correct option is A $x=2m$

We have been given,
$\lambda =x^2-4x+4=(x-2{)}^2$
If we draw the graph of $\lambda$ vs $x$, we get


From the figure we can say that, the rod is non-uniform but load is symmetric about $x=2m$, hence center of mass will be at $x=2m$.