A straight rod of length L has one of its end at the origin and the other at `X=L`. If the mass per unit length of the rod is given by `Ax` where A is constant, where is its centre of mass?

Options

A. `L/3`
B. `L/2`
C. `(2L)/(3)`
D. `(3L)/4`

Answer

C

Explanation

`X_(CM) = (intXdm)/(intdm) = (int_(0)^(L) (Ax).x.dx)/int_(0)^(L)(Ax).dx = (2L)/3`