# Metrology and Inspection

 Question 1
A 76.2 mm gauge block is used under one end of a 254 mm sine bar with roll diameter of 25.4 mm. The height of gauge blocks required at the other end of the sine bar to measure an angle of $30^{\circ}$ is __________mm (round off to two decimal places).
 A 203.2 B 145.6 C 214.3 D 542.6
GATE ME 2021 SET-2   Manufacturing Engineering
Question 1 Explanation:

\begin{aligned} \sin 30^{\circ} &=\frac{h_{1}}{254} \\ \text{or}\qquad h_{1} &=254 \sin 30^{\circ}=127 \mathrm{~mm} \\ H_{2} &=76.2+127=203.2 \mathrm{~mm} \end{aligned}\\ Case II:

\begin{aligned} \sin 30^{\circ} &=\frac{76.2-h_{1}}{254} \\ \text{or}\qquad h_{1} &=76.2-254 \sin 30^{\circ}\\ &=-50.8 \mathrm{~mm} \end{aligned}
Which is not feasible
Therefore final answer 203.2 mm.
 Question 2
The allowance provided in between a hole and a shaft is calculated from the difference between
 A lower limit of the shaft and the upper limit of the hole B upper limit of the shaft and the upper limit of the hole C upper limit of the shaft and the lower limit of the hole D lower limit of the shaft and the lower limit of the hole
GATE ME 2021 SET-2   Manufacturing Engineering
Question 2 Explanation:
It is minimum clearance or maximum interference. It is the intentional difference between the basic dimensions of the mating parts. The allowance may be positive or negative.

 Question 3
Two smooth identical spheres each of radius 125 mm and weight 100 N rest in a horizontal channel having vertical walls. The distance between vertical walls of the channel is 400 mm.

The reaction at the point of contact between two spheres is _______N (round off to one decimal place).
 A 110 B 125 C 258 D 324
GATE ME 2021 SET-1   Manufacturing Engineering
Question 3 Explanation:

\begin{aligned} B C &=250^{2}-150^{2} \\ \cos \theta &=\frac{200}{250} \\ \theta &=36.869^{\circ} \end{aligned}

\begin{aligned} R_{2} \cos \theta &=100 \\ R_{2} &=\frac{100 \times 250}{200}=125 \mathrm{~N} \end{aligned}
 Question 4
Consider the surface roughness profile as shown in the figure.

The center line average roughness ($R_a \text{ in }\mu m$) of the measured length (L) is
 A 0 B 1 C 2 D 4
GATE ME 2021 SET-1   Manufacturing Engineering
Question 4 Explanation:
$R_{G}=\frac{\sum_{i=1}^{n} y}{n}=\frac{4}{4}=1$
 Question 5
Two rollers of diameters $D_1$ (in mm) and $D_2$ (in mm) are used to measure the internal taper angle in the V-groove of a machined component. The heights $H_1$ (in mm) and $H_2$ (in mm) are measured by using a height gauge after inserting the rollers into the same V-groove as shown in the figure.

Which one of the following is the correct relationship to evaluate the angle $\alpha$ as shown in the figure?
 A $\sin \alpha =\frac{(D_1-D_2)}{2(H_1-H_2)-(D_1-D_2)}$ B $\cos \alpha =\frac{(D_1-D_2)}{2(H_1-H_2)-2(D_1-D_2)}$ C $cosec\; \alpha =\frac{(H_1-H_2)-(D_1-D_2)}{2(D_1-D_2)}$ D $\sin \alpha =\frac{(H_1-H_2)}{(D_1-D_2)}$
GATE ME 2020 SET-2   Manufacturing Engineering
Question 5 Explanation:

\begin{aligned} O B &=\left(H_{1}-\frac{D_{1}}{2}\right)-\left(H_{2}-\frac{D_{2}}{2}\right)\\ &=\left(H_{1}-H_{2}\right)-\left(\frac{D_{1}-D_{2}}{2}\right) \\ O A &=\frac{D_{1}-D_{2}}{2} \\ \sin \alpha &=\frac{\frac{\left(D_{1}-D_{2}\right)}{2}}{\left(H_{1}-H_{2}\right)-\frac{\left(D_{1}-D_{2}\right)}{2}} \\ \sin \alpha &=\frac{\left(D_{1}-D_{2}\right)}{2\left(H_{1}-H_{2}\right)-\left(D_{1}-D_{2}\right)} \end{aligned}
 Question 6
The figure below shows a symbolic representation of the surface texture in a perpendicular lay orientation with indicative values (I through VI) marking the various specifications whose definitions are listed below.

P: Maximum Waviness Height (mm);
Q: Maximum Roughness Height (mm);
R: Minimum Roughness Height (mm);
S: Maximum Waviness Width (mm);
T: Maximum Roughness Width (mm);
U: Roughness Width (mm);

The correct match between the specifications and the symbols (I to VI) is:
 A I-R, II-Q, III-P, IV-S, V-U, VI-T B I-R, II-P, III-U, IV-S, V-T, VI-Q C I-U, II-S, III-Q, IV-T, V-R, VI-P D I-Q, II-U, III-R, IV-T, V-S, VI-P
GATE ME 2020 SET-2   Manufacturing Engineering
Question 6 Explanation:

I-R, II-Q, III-P, IV-S, V-U, VI-T
 Question 7
The most common limit gage used for inspecting the hole diameter is
 A Snap gage B Ring gage C Plug gage D Master gage
GATE ME 2019 SET-2   Manufacturing Engineering
Question 7 Explanation:
Plug gauges used for hole & Ring gauge used for shaft
 Question 8
The height (in mm) for a 125 mm sine bar to measure a taper of $27^{\circ}{32}'$ on a flat work piece is _______ (correct to three decimal places).
 A 32.247 B 48.358 C 57.782 D 64.124
GATE ME 2018 SET-1   Manufacturing Engineering
Question 8 Explanation:
(57.782)
\begin{aligned} \theta &=27^{\circ} 32^{\prime} \\ &=27+\left(\frac{32}{60}\right)^{\circ}=27.533^{\circ} \\ \text{In sine bar,}\quad \sin \theta &=\frac{H}{L}\\ \therefore \quad \sin 27.533^{\circ} &=\frac{H}{125} \\ H &=57.782427 \\ H & \approx 57.782 \mathrm{mm} \end{aligned}
 Question 9
A cylindrical pin of $25_{+0.020}^{+0.010}\,mm$ diameter is electroplated. Plating thickness is $2.0^{\pm 0.005}$ mm.Neglecting the gauge tolerance, the diameter (in mm, up to 3 decimal points accuracy) of the GO ring gauge to inspect the plated pin is _______
 A 29.03 B 25.02 C 27.03 D 23.03
GATE ME 2017 SET-2   Manufacturing Engineering
Question 9 Explanation:
GO ring gauge will inspect maximum metal
conditions i.e. UL of shaft i.e. Largest size after
platting.

UL after platting $=25.02+2.005+2.005 \mathrm{mm}= 29.030 \mathrm{mm}$
 Question 10
Assume that the surface roughness profile is triangular as shown schematically in the figure. If the peak to valley height is $20\,\mu m$, The central line average surface roughness $R_{a}(in\,\mu m)$ is
 A 5 B 6.67 C 10 D 20
GATE ME 2017 SET-1   Manufacturing Engineering
Question 10 Explanation:
$R_{a}=\frac{h}{4}=\frac{20}{4}=5 \mu \mathrm{m}$
There are 10 questions to complete.