Question

A thin rod of length `6 m` is lying along the x-axis with its ends at `x = 0` and `x = 6m`. It linear density (mass/length) varies with x as `kx^(4)`. Find the position of centre of mass of rod in meters.

Answer 1

Correct Answer - `5 m`
`x_(cm) = (intxdm)/(intdm) = (int_(0)^(6) x(kx^(4)dx))/(int_(0)^(6) (kx^(4)dx)) = (int_(0)^(6)x^(5)dx)/(int_(0)^(6)x^(4)dx) = ((x^(6)/(6))_(0)^(6))/((x^(5)/(5))_(0)^(6))5m`