Chapter 31, Problem 15A

To determine

(a)

The vernier caliper setting.

Answer to Problem 15A

The vernier caliper setting is $1.894^{″}$.

Explanation of Solution

Given information:

The zero vernier graduation lies between these main scale graduations is $1.875^{″}-1.900^{″}$ and the vernier graduation that coincides with the main scale is $19$.

Write the expression for the vernier caliper measurement.

  $\text{VCM}=\left({\text{MSR}}_{\min }+\text{VC}\times \text{LC}\right)$   ...........(I)

Here, the vernier caliper measurement is $\text{VCM}$, the minimum value of main scale reading is ${\text{MSR}}_{\min }$, the vernier coincidence is $\text{VC}$ and the least count of the vernier caliper is $\text{LC}$.

Calculation:

Substitute $1.875^{″}$ for ${\text{MSR}}_{\min }$, $19$ for $\text{VC}$ and $0.001^{″}$ for $\text{LC}$ in Equation (I).

  $\begin{array}{c}\text{VCM}=\left[1.875^{″}+\left(19\times 0.001^{″}\right)\right]\\ =\left(1.875^{″}+0.019^{″}\right)\\ =1.894^{″}\end{array}$

Conclusion:

The vernier caliper setting is $1.894^{″}$.

To determine

(b)

The vernier caliper setting.

Answer to Problem 15A

The vernier caliper setting is $3.046^{″}$.

Explanation of Solution

Given information:

The zero vernier graduation lies between these main scale graduations is $3.025^{″}-3.050^{″}$ and the vernier graduation that coincides with the main scale is $21$.

Calculation:

Substitute $3.025^{″}$ for ${\text{MSR}}_{\min }$, $21$ for $\text{VC}$ and $0.001^{″}$ for $\text{LC}$ in Equation (I).

  $\begin{array}{c}\text{VCM}=\left[3.025^{″}+\left(21\times 0.001^{″}\right)\right]\\ =3.025^{″}+0.021^{″}\\ =3.046^{″}\end{array}$

Conclusion:

The vernier caliper setting is $3.046^{″}$.

To determine

(c)

The vernier caliper setting.

Answer to Problem 15A

The vernier caliper setting is $0.056^{″}$.

Explanation of Solution

Given information:

The zero vernier graduation lies between these main scale graduations is $0.050^{″}-0.075^{″}$ and the vernier graduation that coincides with the main scale is $6$.

Calculation:

Substitute $0.050^{″}$ for ${\text{MSR}}_{\min }$, $6$ for $\text{VC}$ and $0.001^{″}$ for $\text{LC}$ in Equation (I).

  $\begin{array}{c}\text{VCM}=\left[0.050^{″}+\left(6\times 0.001^{″}\right)\right]\\ =0.050^{″}+0.006^{″}\\ =0.056^{″}\end{array}$

Conclusion:

The vernier caliper setting is $0.056^{″}$.

To determine

(d)

The vernier caliper setting.

Answer to Problem 15A

The vernier caliper setting is $5.786^{″}$.

Explanation of Solution

Given information:

The zero vernier graduation lies between these main scale graduations is $5.775^{″}-5.800^{″}$ and the vernier graduation that coincides with the main scale is $11$.

Calculation:

Substitute $5.775^{″}$ for ${\text{MSR}}_{\min }$, $11$ for $\text{VC}$ and $0.001^{″}$ for $\text{LC}$ in Equation (I).

  $\begin{array}{c}\text{VCM}=\left[5.775^{″}+\left(11\times 0.001^{″}\right)\right]\\ =5.775^{″}+0.011^{″}\\ =5.786^{″}\end{array}$

Conclusion:

The vernier caliper setting is $5.786^{″}$.

To determine

(e)

The vernier caliper setting.

Answer to Problem 15A

The vernier caliper setting is $1.232^{″}$.

Explanation of Solution

Given information:

The zero vernier graduation lies between these main scale graduations is $1.225^{″}-1.250^{″}$ and the vernier graduation that coincides with the main scale is $7$.

Calculation:

Substitute $1.225^{″}$ for ${\text{MSR}}_{\min }$, $7$ for $\text{VC}$ and $0.001^{″}$ for $\text{LC}$ in Equation (I).

  $\begin{array}{c}\text{VCM}=\left[1.225^{″}+\left(7\times 0.001^{″}\right)\right]\\ =1.225^{″}+0.007^{″}\\ =1.232^{″}\end{array}$

Conclusion:

The vernier caliper setting is $1.232^{″}$.

To determine

(f)

The vernier caliper setting.

Answer to Problem 15A

The vernier caliper setting is $0.091^{″}$.

Explanation of Solution

Given information:

The zero vernier graduation lies between these main scale graduations is $0.075^{″}-0.100^{″}$ and the vernier graduation that coincides with the main scale is $16$.

Calculation:

Substitute $0.075^{″}$ for ${\text{MSR}}_{\min }$, $16$ for $\text{VC}$ and $0.001^{″}$ for $\text{LC}$ in Equation (I).

  $\begin{array}{c}\text{VCM}=\left[0.075^{″}+\left(16\times 0.001^{″}\right)\right]\\ =0.075^{″}+0.016^{″}\\ =0.091^{″}\end{array}$

Conclusion:

Therefore, the vernier caliper setting is $0.091^{″}$.

To determine

(g)

The vernier caliper setting.

Answer to Problem 15A

The vernier caliper setting is $3.004^{″}$.

Explanation of Solution

Given information:

The zero vernier graduation lies between these main scale graduations is $3.000^{″}-3.025^{″}$ and the vernier graduation that coincides with the main scale is $4$.

Calculation:

Substitute $3.000^{″}$ for ${\text{MSR}}_{\min }$, $4$ for $\text{VC}$ and $0.001^{″}$ for $\text{LC}$ in Equation (I).

  $\begin{array}{c}\text{VCM}=\left[3.000^{″}+\left(4\times 0.001^{″}\right)\right]\\ =3.000^{″}+0.004^{″}\\ =3.004^{″}\end{array}$

Conclusion:

Therefore, the vernier caliper setting is $3.004^{″}$.

To determine

(h)

The vernier caliper setting.

Answer to Problem 15A

The vernier caliper setting is $2.659^{″}$.

Explanation of Solution

Given information:

The zero vernier graduation lies between these main scale graduations is $2.650^{″}-2.675^{″}$ and the vernier graduation that coincides with the main scale is $9$.

Calculation:

Substitute $2.650^{″}$ for ${\text{MSR}}_{\min }$, $9$ for $\text{VC}$ and $0.001^{″}$ for $\text{LC}$ in Equation (I).

  $\begin{array}{c}\text{VCM}=\left[2.650^{″}+\left(9\times 0.001^{″}\right)\right]\\ =2.650^{″}+0.009^{″}\\ =2.659^{″}\end{array}$

Conclusion:

The vernier caliper setting is $2.659^{″}$.

To determine

(i)

The vernier caliper setting.

Answer to Problem 15A

The vernier caliper setting is $1.013^{″}$.

Explanation of Solution

Given information:

The zero vernier graduation lies between these main scale graduations is $1.000^{″}-1.025^{″}$ and the vernier graduation that coincides with the main scale is $13$.

Calculation:

Substitute $1.000^{″}$ for ${\text{MSR}}_{\min }$, $13$ for $\text{VC}$ and $0.001^{″}$ for $\text{LC}$ in Equation (I).

  $\begin{array}{c}\text{VCM}=\left[1.000^{″}+\left(13\times 0.001^{″}\right)\right]\\ =1.000^{″}+0.013^{″}\\ =1.013^{″}\end{array}$

Conclusion:

The vernier caliper setting is $1.013^{″}$.

To determine

(j)

The vernier caliper setting.

Answer to Problem 15A

The vernier caliper setting is $5.993^{″}$.

Explanation of Solution

Given information:

The zero vernier graduation lies between these main scale graduations is $5.975^{″}-6.000^{″}$ and the vernier graduation that coincides with the main scale is $18$.

Calculation:

Substitute $5.975^{″}$ for ${\text{MSR}}_{\min }$, $18$ for $\text{VC}$ and $0.001^{″}$ for $\text{LC}$ in Equation (I).

  $\begin{array}{c}\text{VCM}=\left[5.975^{″}+\left(18\times 0.001^{″}\right)\right]\\ =5.975^{″}+0.018^{″}\\ =5.993^{″}\end{array}$

Conclusion:

The vernier caliper setting is $5.993^{″}$.

To determine

(k)

The vernier caliper setting.

Answer to Problem 15A

The vernier caliper setting is $2.833^{″}$.

Explanation of Solution

Given information:

The zero vernier graduation lies between these main scale graduations is $2.825^{″}-2.850^{″}$ and the vernier graduation that coincides with the main scale is $8$.

Calculation:

Substitute $2.825^{″}$ for ${\text{MSR}}_{\min }$, $8$ for $\text{VC}$ and $0.001^{″}$ for $\text{LC}$ in Equation (I).

  $\begin{array}{c}\text{VCM}=\left[2.825^{″}+\left(8\times 0.001^{″}\right)\right]\\ =2.825^{″}+0.008^{″}\\ =2.833^{″}\end{array}$

Conclusion:

The vernier caliper setting is $2.833^{″}$.

To determine

(l)

The vernier caliper setting.

Answer to Problem 15A

The vernier caliper setting is $4.951^{″}$.

Explanation of Solution

Given information:

The zero vernier graduation lies between these main scale graduations is $4.950^{″}-4.975^{″}$ and the vernier graduation that coincides with the main scale is $1$.

Calculation:

Substitute $4.950^{″}$ for ${\text{MSR}}_{\min }$, $1$ for $\text{VC}$ and $0.001^{″}$ for $\text{LC}$ in Equation (I).

  $\begin{array}{c}\text{VCM}=\left[4.950^{″}+\left(1\times 0.001^{″}\right)\right]\\ =4.950^{″}+0.001^{″}\\ =4.951^{″}\end{array}$

Conclusion:

The vernier caliper setting is $4.951^{″}$.