A rod of length L is positioned along the X-axis between x = 0 and x = L . The linear density (mass/length) of the rod varies with the distance x from the origin as = a + bx . Determine the SI units of a and b .

Step-by-step solution

The linear density is defined as mass per unit length, so its SI unit is kg/m . According to the principle of dimensional homogeneity, each term in the equation = a + bx must have the same unit. Therefore, the unit of a is the same as the unit of , which is kg/m . Similarly, the unit of the term bx must be kg/m . Since x represents distance, its SI unit is m . Unit of b = Unit of Unit of x = kg/m m = kg/m ^2 . Thus, the SI units of a and b are kg/m and kg/m ^2 respectively.