Help please with this problem?

Question

A rod of length 20.00 cm has linear density (mass per length) given by

λ = 50.0 + 20.5x

where x is the distance from one end, and λ is measured in grams/meter.

(a) What is its mass?

 _____g

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

 _____m

Answer 1

Hello, Daniel,

If I understood your data correctly, I calculate a mass of 54.1g (with 4 sig figs). The linear density formula requires the input for length to be in meters, so 20.00 cm becomes 0.0200 m. The equation gives 50.41 g for the 20.00 cm length of rod.

Since the mass is a linear function of distance, the rod is symmetrical, so the center of gravity would be halfway down the rod (10.0 centimeters).

I hope this helps,

Bob