Question

The table gives the initial lengths of three rods and the changes in their lengths when forces are applied to their ends to put them under strain. Rank the rods according to their strain, greatest first.

Short answer

The greatest strain is for rods A and B, and strain in rod C is the least; thus, the rank is A = B > C .

Step-by-step solution

The given data

Initial length and the change in length are given for each rod A, B, and C.

Understanding the concept of strain

We use the definition of strain, which is a fractional increase in length, to calculate the required rank according to their strain measures.

Formulae:

The strain applied on a body due to a change in the length, Strain$=\frac{∆L}{L}$ (i)

Calculation of the rank of the rods according to their strain value

Using the given data in equation (i), the strain of rod A can be calculated as follows:

${\mathrm{Strain}}_A=\frac{∆{\mathrm{L}}_0}{2{\mathrm{L}}_0}$

Using the given data in equation (i), the strain of the rod B can be calculated as follows:

$$\begin{gathered} {\mathrm{Strain}}_B=\frac{2∆{\mathrm{L}}_{\mathit{0}}}{4L_{\mathit{0}}} \\ =\frac{∆{\mathrm{L}}_0}{2{\mathrm{L}}_0} \end{gathered}$$

Using the given data in equation (i), the strain of the rod C can be calculated as follows:

$$\begin{gathered} {\mathrm{Strain}}_B=\frac{4∆{\mathrm{L}}_{\mathit{0}}}{10L_{\mathit{0}}} \\ =\frac{2∆{\mathrm{L}}_0}{5{\mathrm{L}}_0} \end{gathered}$$

Hence, the rank value according to their strain is A = B > C .