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Question

Find the position of the centre of mass of T - shaped lamina of negligible thickness as shown in figure. Assume the origin to be at the intersection of axes and take the mass density of the lamina, σ=1 kg/m2


A
(0,6.5) m
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B
(0,6) m
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C
(0,5.28) m
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D
(0,4.55) m
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Solution

The correct option is C (0,5.28) m
The T - shaped lamina is divided into two pieces of mass m1 and m2


m1=σ× Area of part 1
=1×(6×2)
=12 kg
m2=σ× Area of part 2
=1×(8×2)
=16 kg
Taking origin at point O,
Centre of mass of part 1 is (x1,y1)=(0,3) m
Centre of mass of part 2 is (x2,y2)=(0,7) m

x - coordinate of center of mass will be 0 ( lamina is symmetric about y - axis) i.e xcom=0 m
and y - coordinate of centre of mass is
ycom=m1y1+m2y2m1+m2
=12×3+16×712+16=14828 m
= 5.28 m
So, position of centre of mass of T- shaped lamina is (xcom,ycom)=(0,5.28) m

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