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

Answer

`5 m`

Explanation

`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`