Question

# Find the centre of mass of uniform L-shaped lamina (a thin flat plate) with dimensions as shown in figure. The mass of lamina is 3 kg

A

(56m,56m)

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B

(65m,66m)

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C

(52m,56m)

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D

(53m,65m)

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Solution

## The correct option is A (56m,56m) The plate is 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 = 2m2 with its centroid C1(1,12) and A1 = 1 × 1 = 1m2 with its centroid C2(12,32) The centroid of whole plate can be defined as; ¯¯¯x = A1x1 + A2x2A1 + A2 = 2 × 1 + 1 × 122 + 1 = 56m and ¯¯¯y = A1y1 + A2y2A1 + A2 = 2 × 12 + 1 × 322 + 1 = 56m

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