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Question

A uniform rectangular lamina ABCD is of mass M, length a and breadth b, as shown in the figure. If the shaded portion HBGO is cut-off, the coordinates of the centre of mass of the remaining portion will be

A
(2a3,2b3)
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B
(5a3,5b3)
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C
(3a4,3b4)
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D
(5a12,5b12)
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Solution

The correct option is D (5a12,5b12)
Let the mass of rectangular lamina ABCD be M, length be a and breadth be b
The centre of mass of rectangular lamina ABCD is at point (x1,y1)=(a2,b2)


Centre of mass of the rectangular lamina HBGO is (x2,y2)=(3a4,3b4)
Mass of rectangular lamina HBGO= M4
xcoordinate of c.o.m after mass removal is given by
xcm=m1x1m2x2m1m2
x=Ma2M4×3a4MM4=a23a1634=5a12 Units
y coordinate of c.o.m after mass removal is given by
ycm=m1y1m2y2m1m2
y=Mb2M4×3b4MM4=5b12 Units

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