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A non-uniform rod of length L has linear mass density lambda = K*x²/L, where K is a constant and x is the distance from one end. Find the distance of its centre of mass from that end.

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

Correct answer: 3L/4

Solution

x_cm = (integral 0..L x*x² dx)/(integral 0..L x² dx) = (L⁴/4)/(L³/3) = 3L/4.

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