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Question

Find coordinates of the centre of mass of a uniform Lshaped lamina (a thin flat plate) wrt origin, having dimensions as shown in figure. (Consider mass of lamina as 3m kg)

A
(56;56)
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B
(56,76)
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C
(53,56)
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D
(56,57)
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Solution

The correct option is C (56;56)
From figure L shaped lamina can be considered as combination of
(i)A square of mass m having centre at (12,32)
(ii)A rectangle of mass 2m having centre at(1,12)
( Area of rectangle is double that of area of square. So, mass of the rectangle is also double to that of mass of square)

Finding position of COM,
xcm=2m×1+m×123m=56
ycm=2m×12+m×323m=56


So, Coordinates of COM are (56,56)

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