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.

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