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A rod of length 2 m at 0 deg C has a position-dependent linear expansion coefficient alpha = (3x + 2) * 10⁻⁶ per deg C, where x is the distance in cm from one end. Find the length of the rod at 20 deg C.

1. 2.124 m
2. 3.24 m
3. 2.0120 m
4. 3.124 m

Correct answer: 2.0120 m

Solution

Integrating the position-dependent expansion gives an elongation of about 1.2 cm, so the rod becomes 2.0120 m at 20 deg C.

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