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Question

Two uniform rectangular plates having mass density (mass/area) 2 kg/m2 and 1 kg/m2 are joined together to form the L- shaped lamina as shown in the figure. Find the coordinates of centre of mass of the L-shaped lamina.


A
(1711,8322) m
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B
(267,4314)m
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C
(267,8322)m
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D
(137,4314)m
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Solution

The correct option is D (137,4314)m

Area of plate 1 , A1=(6×1)=6 m2
Area of plate 2 , A2=(8×2)=16 m2
Mass of plate 1 , m1=(A1×σ1)=6×2=12 kg
Mass of plate 2 , m2=(A2×σ2)=16×1=16 kg

Centre of mass of a uniform rectangular plate is given by: (l2,b2)
COM of plate 1 (x1,y1)=(3,0.5) m
COM of plate 2 (x2,y2)=(1,5) m

Now, replacing the respective plates by point masses placed at their respective COM :
x- coordinate of com of L- shaped lamina:
xCM=m1x1+m2x2m1+m2=12×3+16×112+16=5228xCM=137 m
and y- coordinate of com of L- shaped lamina:
yCM=m1y1+m2y2m1+m2=12×0.5+16×512+16=8628yCM=4314 m
Hence, COM of L- shaped lamina is given by
(xCM,yCM)=(137,4314) m

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