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A thin one-dimensional rod AB of length L has a linear mass density that varies with distance x measured from end A as rho = rho0*(1 - x²/L²). What is the distance of the centre of mass of the rod from end A?

1. 3L/8
2. L/2
3. 3L/5
4. 5L/8

Correct answer: 3L/8

Solution

Treating the rod as a continuous mass distribution, the centre of mass is the mass-weighted average position; the varying density shifts it toward end A, giving 3L/8.

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