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A rod of length 1 m has a position-dependent coefficient of linear expansion alpha = x/5000 (x in metres, measured from one end). Find the increase in the rod's length when its temperature is raised by 100 deg C.

1. 1 cm
2. 0.5 cm
3. 1.5 cm
4. 0.75 cm

Correct answer: 1 cm

Solution

Integrating the variable expansion gives deltaL = deltaT * (1/2)/5000 = 100/10000 = 0.01 m = 1 cm.

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