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Example: Find the centre of mass of a uniform stick 2 m long and 4 kg in mass, with one end at x = 0 m and the other at x = 2 m. Steps: 1. Total mass M = 4 kg. 2. For a uniform stick, density is constant, so dm = (M/L) dx = (4 kg / 2 m) dx = 2 kg/m · dx. 3. The x‑coordinate of the centre of mass: x_cm = (1/M) ∫_0^2 x dm. 4. Substitute dm: x_cm = (1/4) ∫_0^2 x (2 dx) = (1/4)·2 ∫_0^2 x dx. 5. Evaluate the integral: ∫_0^2 x dx = [x^2/2]_0^2 = (4/2) - 0 = 2. 6. Compute x_cm: x_cm = (1/4)·2·2 = 1 m. Answer: The centre of mass is 1 m from the left end, exactly in the middle of the stick.