Question

A thin rod of length L is lying along the x - axis with its ends at x =0 and x= L. Its linear density (mass/length) varies with x as ${\left(\frac{x}{L}\right)}^n$, where k is a constant and n can be zero or any positive number. If the position $x_{cm}$ of the centre of mass of the rod is plotted against n, which of the following graphs best approximates the dependence of $x_{cm}$ on n

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

$X_{CM}=\frac{\int xdm}{\int dm}$

If n = 0, then $X_{c}m=\frac{L}{2}$

As n increases, the centre of mass shift away from $x=\frac{L}{2}$ which only (a) option is satisfying.