    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=5228∴xCM=137 m and y- coordinate of com of L- shaped lamina: yCM=m1y1+m2y2m1+m2=12×0.5+16×512+16=8628∴yCM=4314 m Hence, COM of L- shaped lamina is given by (xCM,yCM)=(137,4314) m  Suggest Corrections  0      Similar questions  Related Videos   Integrating Solids into the Picture
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