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A uniform L-shaped thin lamina of total mass 3 kg is made of three identical 1 m × 1 m squares as shown in the figure. Taking the axes as marked, find the coordinates (X, Y) of its centre of mass. 
A(1/2, 1/2) m
B(5/6, 5/6) m
C(1, 1) m
D(3/2, 3/2) m
Answer & Solution
Correct answer: B. (5/6, 5/6) m
The lamina is three unit squares of 1 kg each, with geometric centres at (1/2, 1/2), (3/2, 1/2) and (1/2, 3/2). X = [1·(1/2) + 1·(3/2) + 1·(1/2)] / 3 = (5/2)/3 = 5/6 m. By the same calculation Y = 5/6 m. The COM is therefore at (5/6, 5/6) m — not at the geometric centre of the bounding square, because the L is asymmetric about (1, 1).
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