GATE ME 2014 Set 3 — Question 63
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Metrology, CIM & Additive Mfg → Metrology & Inspection → Linear & Angular Measurement
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Question
The diameter of a recessed ring was measured by using two spherical balls of diameter mm and mm as shown in the figure. The distance mm and mm. The diameter (, in mm) of the ring gauge is _______
Correct answer
92 to 94
Solution
Given:
Diameter of ball 1, mm radius mm
Diameter of ball 2, mm radius mm
Distances from the top of the ring to the top of the balls: mm, mmLet be the total depth of the recessed ring.
From the geometry shown in the figure:
mmThe distance between the centers of the two balls when they are in contact is:
mmThe horizontal distance between the centers () is calculated using the Pythagorean theorem:
mmThe diameter of the ring gauge is the sum of the radii and the horizontal distance between the centers (since the balls touch opposite walls and each other):
mmThe calculated value is approximately 93.3 mm, which falls within the official range of 92 to 94.
Diameter of ball 1, mm radius mm
Diameter of ball 2, mm radius mm
Distances from the top of the ring to the top of the balls: mm, mmLet be the total depth of the recessed ring.
From the geometry shown in the figure:
- The height of the center of ball 1 from the bottom is .
- The height of the center of ball 2 from the bottom is .
mmThe distance between the centers of the two balls when they are in contact is:
mmThe horizontal distance between the centers () is calculated using the Pythagorean theorem:
mmThe diameter of the ring gauge is the sum of the radii and the horizontal distance between the centers (since the balls touch opposite walls and each other):
mmThe calculated value is approximately 93.3 mm, which falls within the official range of 92 to 94.
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