Chapter 33, Problem 1A

To determine

The vernier micrometer reading.

Answer to Problem 1A

The vernier micrometer reading is $0.188\text{in}$.

Explanation of Solution

Given information:

The micrometer scale reading is $0.001\text{in}$, the barrel reading is $0.175\text{in}$ and the thimble reading is $0.008\text{in}$.

The below figure represent the setting of a gage.

Figure-(1)

Write the expression for the Vernier scale coincidence.

  $\text{VR}=\text{GR}\times x$   .........(I)

Here, the graduated scale reading is $\text{GR}$ and the micrometer scale is $x$.

Write the expression for the vernier scale reading.

  $\text{VSR}=\text{BR}+\text{TR}+\text{VR}$   .........(II)

Here, thimble scale reading is $\text{TR}$ and the barrel scale reading is $\text{BR}$.

Here, barrel scale reading is $\text{BR}$.

Substitute $\text{GR}\times x$ for $\text{VR}$ in Equation (II).

  $\text{VSR}=\text{BR}+\text{TR}+\left(\text{GR}\times x\right)$ ........ (III)

Calculation:

Substitute $0.175\text{in}$ for $\text{BR}$, $0.008\text{in}$ for $\text{TR}$, $5$ for $\text{GR}$, and $0.001\text{in}$ for $x$ in Equation (III).

  $\begin{array}{c}\text{VSR}=\left(0.175\text{in}\right)+\left(0.008\text{in}\right)+\left(5\times 0.001\text{in}\right)\\ =\left(0.175\text{in}\right)+\left(0.008\text{in}\right)+\left(0.005\text{in}\right)\\ =0.188\text{in}\end{array}$

Conclusion:

The vernier micrometer reading is $0.188\text{in}$.