Understanding Tolerance in Dimensions

The question asks us to identify which dimension has the largest tolerance. Tolerance in engineering refers to the total permissible variation allowed in the size of a manufactured part. It is the difference between the maximum and minimum permissible sizes (limits) of a dimension.

Mathematically, tolerance is calculated as:

$$ \text{Tolerance} = \text{Upper Limit} - \text{Lower Limit} $$

Or, using deviations:

$$ \text{Tolerance} = (\text{Nominal Size} + \text{Positive Deviation}) - (\text{Nominal Size} + \text{Negative Deviation}) $$

$$ \text{Tolerance} = \text{Positive Deviation} - \text{Negative Deviation} $$

Let's calculate the tolerance for each option provided. The nominal size for all options is 40.

Calculating Tolerance for Each Option

Option 1: 40^{+0.06, -0.02}

• Nominal Size: 40
• Positive Deviation (Upper Deviation): $+0.06$
• Negative Deviation (Lower Deviation): $-0.02$
• Upper Limit: $40 + 0.06 = 40.06$
• Lower Limit: $40 + (-0.02) = 40 - 0.02 = 39.98$
• Tolerance: $40.06 - 39.98 = 0.10$

Option 2: 40^{+0.05, -0.08}

• Nominal Size: 40
• Positive Deviation (Upper Deviation): $+0.05$
• Negative Deviation (Lower Deviation): $-0.08$
• Upper Limit: $40 + 0.05 = 40.05$
• Lower Limit: $40 + (-0.08) = 40 - 0.08 = 39.92$
• Tolerance: $40.05 - 39.92 = 0.13$

Option 3: 40^{-0.01, -0.06}

• Nominal Size: 40
• Positive Deviation (Upper Deviation): $-0.01$
• Negative Deviation (Lower Deviation): $-0.06$
• Upper Limit: $40 + (-0.01) = 40 - 0.01 = 39.99$
• Lower Limit: $40 + (-0.06) = 40 - 0.06 = 39.94$
• Tolerance: $39.99 - 39.94 = 0.05$

Note: In this case, both deviations are negative. The upper limit is the less negative deviation.

Option 4: 40^{+0.01, -0.1}

• Nominal Size: 40
• Positive Deviation (Upper Deviation): $+0.01$
• Negative Deviation (Lower Deviation): $-0.1$
• Upper Limit: $40 + 0.01 = 40.01$
• Lower Limit: $40 + (-0.1) = 40 - 0.1 = 39.90$
• Tolerance: $40.01 - 39.90 = 0.11$

Comparing Tolerances

Let's summarize the calculated tolerances:

Identifying the Largest Tolerance

By comparing the calculated tolerance values (0.10, 0.13, 0.05, and 0.11), we can see that the dimension 40^{+0.05, -0.08} has the largest tolerance, which is $0.13$.