Chapter 8, Problem 4RE

To determine

To determine the total mass of the rod.

Answer to Problem 4RE

The total mass of 2-meter rod is $14$ gram.

Explanation of Solution

Given:

A $2$ -meter rod has a variable density modeled by the function $\rho \left(x\right)=11-4x$ g/m . where $x$ is the distance in meters from the base of the rod.

Calculation:

Since, the variable density (mass per unit length) of a $2$ meter rod is given by

  $\rho \left(x\right)=11-4x$ g/m

The total mass of the rod

  ${\displaystyle \underset{0}{\overset{2}{\int }}\rho \left(x\right)}dx={\displaystyle \underset{0}{\overset{2}{\int }}\left(11-4x\right)}dx={\left|11x-2x^2\right|}_0^2=\left(11\times 2-2{\left(2\right)}^2\right)-\left(0\right)=14$

Therefore, the total mass of 2-meter rod is $14$ gram.