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Question

A uniform L shaped lamina with given dimensions is shown in the figure. Origin is taken at O.


If the mass of the lamina is 6 kg, then the centre of mass of the lamina is located at:

A
(53 m,56 m)
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B
(54 m,56 m)
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C
(53 m,53 m)
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D
(58 m,53 m)
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Solution

The correct option is A (53 m,56 m)
Dividing the given lamina into two rectangular sections of area A1 and A2.

We replace the rectangular section by placing point masses at their respective COM's.


Area of rectangular section A1=4 m2
Area of rectangular section A2=2 m2

Centre of mass of section 1 C1=(x1,y1)=(2 m,12 m)
Centre of mass of section 2 C2=(x2,y2)=(1 m,32 m)

Applying the formula for x and y coordinates of CM for the combination of rectangular sections:

xCM=A1x1+A2x2A1+A2=(4×2)+(2×1)4+2=106=53 m
yCM=A1y1+A2y2A1A2=(4×12)+(2×32)4+2=56 m

The coordinates of the centre of mass for given shape is:
(xCM,yCM)=(53 m,56 m)

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