Question

Consider a rod of length L with a non-uniform mass distribution given by λ=A+Bx² where A and B are positive constants, and x=0 from the left end. 25% Part (a) What are the units of A ?

Answer 1

The constant A in the linear mass density function has units of mass per length, such as kilograms per meter (kg/m) in the SI system.

Step-by-step explanation:

The question concerns the units of the constant A in the linear mass density function λ(x) = A + Bx² of a rod with non-uniform mass distribution. The linear mass density function represents the mass per unit length along a rod, which is expressed in units of mass per length (e.g., kg/m in the SI system). Since the term Bx² has units of [B] • [x]², where [B] are the units of B and [x] are the units of length, the units of B must be such that they cancel the units of x², leaving the units of mass per length. Therefore, the constant A must have the same units as λ(x), which are units of mass per length (e.g., kg/m).