Question

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.
A. 5m
B. 3m
C. 2m
D. 4m

Answer 1

Correct Answer - A
`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))^(6))/(((x^(5))/(5))_(0)^(6))=5m`