A rod of length 39.0 cm has linear density (mass-per-length) given by the following equation, where x is the distance from one end.

Question

ë = 50.0 g/m + 21.0x g/m2

(a) What is its mass?
(b) How far from the x = 0 end is its center of mass?

I think you would plug in the 39cm for the x in the equation, but change it to meters first of course. The problem is how do you just get it in grams then because the units you get are g/m. I'm not sure how to even start with the center of mass.

Answer 1

You need to compute the integral of the linear density from x = 0 to x = 39 cm to obtain the mass.

The center of mass is the integral of the linear density times x from x = 0 to x = 39 cm, divided by the mass.