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Fundamentals Of Physics
Found in: Page 541

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Short Answer

A steel rod is 3.00 cm in diameter at 25.00oC. A brass ring has an interior diameter of 2.992 cm at 25.00oC. At what common temperature will the ring just slide onto the rod?

The temperature at which ring just slides into the rod is 360.0oC

See the step by step solution

Step by Step Solution

Step 1: The given data

  1. Diameter of the steel rod at 25oC is Ds=3.000 cm
  2. Diameter of the brass ring at 25oC is Db=2.992 cm
  3. Expansion coefficient for steel is αs=11×10-6/Co
  4. Expansion coefficient for brass is αb=19×10-6/Co

Step 2: Understanding the concept of thermal expansion

When an object's temperature changes, it expands and grows larger, a process known as thermal expansion. Thermal expansion can be occurring due to an increase in temperature. For the given problem, we have to use the formula for linear expansion to calculate the final temperature.


The linear expansion of diameter of a body, D=T …(i)

Where α is the coefficient of linear expansion of body, T is the temperature difference and D is the diameter

Step 3: Calculation of the temperature

The total length after expansion is given as:

D=Ds+Ds=Ds+DsαsT..............a from equationi, the change of expansion

The total length after expansion is given as:

D=Db+Db=Db+DbαbT..............b from equationi, the change of expansion

The rod will fit through the ring only if the diameter of the ring and the rod is the same after the expansion so that, from equations (a) and (b), it is given as:


By substituting the given values in the above equation, we get the temperature change as:

T=3.000 cm-2.992 cm2.992 cm×19×10-6/Co-3.000 cm×11×10-6/Co=0.008 cm56.848-33×10-6 cm/Co=0.008oC23.848×10-6=335.0oC

Using this value, we can calculate the total temperature is given as:


Hence, the value of the temperature is 360.0oC

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