What is the expression for the linear mass density mu of a string?

What is the expression for the linear mass density mu of a string?

• A. mu = m/L
• B. mu = L/m
• C. mu = m
• D. mu = m*L

Answer: (A)

Linear mass density tells you how much mass sits in each unit of length along the string. Since the string has total mass m and total length L, the amount of mass per unit length is m divided by L. So mu = m/L, with units of kilograms per meter. If you tried the other expressions, they don’t fit the idea of mass per length: L/m would describe length per mass, not mass per length; m alone ignores how long the string is; m times L would mix mass and length in a way that doesn’t correspond to a density.

Linear mass density tells you how much mass sits in each unit of length along the string. Since the string has total mass m and total length L, the amount of mass per unit length is m divided by L. So mu = m/L, with units of kilograms per meter.

If you tried the other expressions, they don’t fit the idea of mass per length: L/m would describe length per mass, not mass per length; m alone ignores how long the string is; m times L would mix mass and length in a way that doesn’t correspond to a density.