A uniform triangular lamina has vertices A(0,0), B(6,0) and C(0,6). A smaller triangular lamina with vertices (0,0), (3,0) and (0,3) is removed. If the centre of mass of the remaining lamina is at x(CM) = y(CM) = N/3, find N.
Physics · Center of maas , Momentum and Collision · center of mass and question based on it
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Question

A uniform triangular lamina has vertices A(0,0), B(6,0) and C(0,6). A smaller triangular lamina with vertices (0,0), (3,0) and (0,3) is removed. If the centre of mass of the remaining lamina is at x(CM) = y(CM) = N/3, find N.

Physics · Center of maas , Momentum and Collision · center of mass and question based on it

G1 Physics · Accepted Answer

The area of the large triangle is A₁ = (1/2)(6)(6) = 18 and its centroid is at (2,2). The removed triangle has area A₂ = (1/2)(3)(3) = 9/2 and centroid (1,1). Treat the removed triangle as negative mass, because surface density is uniform. Thus x(CM) = [18(2) − (9/2)(1)]/[18 − 9/2] = (36 − 4.5)/13.5 = 31.5/13.5 = 7/3. By symmetry y(CM) = 7/3. Hence N = 7.