GATE 2022 ME (ME2) – Question 20
A shaft of diameter $25^{-0.04}_{-0.07}$ mm is assembled in a hole of diameter $25^{+0.02}_{-0.00}$ mm. Match the allowance and limit parameter in Column I with its corresponding quantitative value in Column II for this shaft-hole assembly.
| Column I | Column II |
|---|---|
| P. Allowance | 1. 0.09 mm |
| Q. Maximum clearance | 2. 24.96 mm |
| R. Maximum material limit for hole | 3. 0.04 mm |
| 4. 25.0 mm |
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Correct answer: (A) P-3, Q-1, R-4
Explanation
**Step 1: limits of size.**
- Shaft: $25^{-0.04}_{-0.07}$ gives a maximum of $25-0.04=24.96$ mm and a minimum of $25-0.07=24.93$ mm.
- Hole: $25^{+0.02}_{-0.00}$ gives a maximum of $25.02$ mm and a minimum of $25.00$ mm.
**Step 2: match the terms.**
- **P, allowance** is the minimum clearance, the difference between the smallest hole and the largest shaft: $25.00-24.96=0.04$ mm. So P-3.
- **Q, maximum clearance** is the largest hole minus the smallest shaft: $25.02-24.93=0.09$ mm. So Q-1.
- **R, maximum material limit of the hole** is the size at which the hole has the most material, which is its **smallest** diameter, 25.0 mm. So R-4.
The match is **P-3, Q-1, R-4** (option A).