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Question

# Find the c.m. of a uniform L− shaped lamina (a thin flat plate) with dimensions as shown in figure. The mass of lamina is 3 kg And report the sum of x and y coordinates. Answer upto 2 decimal places.

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Solution

## The plate is of uniform density and same thickness everywhere. So its C.M. will coincide with the centroid. Divide the given plate into two parts of area A1 and A2 as shown in figure. We have A1=2×1=2 m2 with its centroid C1(1,1/2) and A2=1×1=1 m2 with its centroid C2(1/2,3/2) The centroid of whole plate can be defined as, xC.M.=A1x1+A2x2A1+A2=2×1+1×122+1=56 m and yC.M.=A1y1+A2y2A1+A2=2×12+1×322+1=56 m Why this question? Tip: About the origin, mass is symmetrically distributed, so x and y coordinates will be same- don't need to calculate individually.

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