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Three identical aluminium rods, each of length 2 m, form an equilateral triangle ABC. Take O (the midpoint of BC) as the origin, with BC along the x-axis and A on the positive y-axis. Find the increase in the y-coordinate of the centre of mass of the system per unit rise in temperature. (alpha_al = 4*sqrt(3) * 10⁻⁶ per deg C.)

1. 2 * 10⁻⁶ m/deg C
2. 4 * 10⁻⁶ m/deg C
3. 6 * 10⁻⁶ m/deg C
4. 8 * 10⁻⁶ m/deg C

Correct answer: 4 * 10⁻⁶ m/deg C

Solution

For the equilateral triangle the centre of mass y-coordinate is L/(2*sqrt(3)); since it scales linearly with size, its rate of increase with temperature is y_cm * alpha = 4 * 10⁻⁶ m/deg C.

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