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Q. 43

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 512

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Short Answer

A brass ring with inner diameter 2.00 cm and outer diameter 3.00 cm needs to fit over a 2.00-cm-diameter steel rod, but at 20C the hole through the brass ring is 50 mm too small in diameter. To what temperature, in C, must the rod and ring be heated so that the ring just barely slips over the rod?

The accurate temperature is

See the step by step solution

Step by Step Solution

Step 1: Description 

A brass ring with inner diameter 2.00 cm and outer diameter 3.00 cm needs to fit over a 2.00-cm-diameter steel rod, but at 20C the hole through the brass ring is 50 mm too small in diameter.

Step 2: Result of finding the temperature 

In increasing the length of the circumference, the requirement for is

There is a matter of change in length of part with linear coefficient would be

Thus, the necessary temperature difference should be

Thus, there can be a replacement of the circumference in both the numerator and denominator and find

Thus, the substitution of numerics in order to find is:

Therefore, in the rod and ring be heated so that the ring just barely slips over the rod.

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