Question

dimensional formula of linear mass density

Answer 1

Consider a long, thin rod of mass {\displaystyle M} M and length {\displaystyle L} L. To calculate the average linear mass density, {\displaystyle {\bar {\lambda }}_{m}} {\bar \lambda }_{m}, of this one dimensional object, we can simply divide the total mass, {\displaystyle M} M, by the total length, {\displaystyle L} L:

{\displaystyle m={\frac {M}{L}}} {\displaystyle m={\frac {M}{L}}}
If we describe the rod as having a varying mass (one that varies as a function of position along the length of the rod, {\displaystyle l} l), we can write:

{\displaystyle m=m(l)} m=m(l)
Each infinitesimal unit of mass, {\displaystyle dm} dm, is equal to the product of its linear mass density, {\displaystyle \lambda _{m}} \lambda_m, and the infinitesimal unit of length, {\displaystyle dl} dl:

{\displaystyle dm=\lambda _{m}dl} dm=\lambda _{m}dl
The linear mass density can then be understood as the derivative of the mass function with respect to the one dimension of the rod (the position along its length {\displaystyle m={\frac {dm}{dl}}} {\displaystyle m={\frac {dm}{dl}}})

Answer 2

Each infinitesimal unit of mass, , is equal to the product of its linear mass density, , and the infinitesimal unit of length, : The SI unit of linear mass density is the kilogram per meter (kg/m). Linear density of fibers and yarns can be measured by many methods.