Suppose we have a rod that is 6 meters long, with density function p(x)=2x+3. What is the center of the mass of the rod?

Question

¯x= 11/3

¯x= 8/3

¯x= 14/3

¯x= 4/3

none of these

Answer 1

The total mass of the rod is the integral from 0 to 6 ∫(2x+3)dx = 54

 

The center of mass is the point m on the rod such that the integral from 0 to 6 ∫(x-m)(2x+3)dx = 0. The is the point m where the moment is zero. This integral 198-54m=0 or m= 11/3