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=1kg/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) =12kg m2=σ× Area of part 2 =1×(8×2) =16kg
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=0m
and y - coordinate of centre of mass is ycom=m1y1+m2y2m1+m2 =12×3+16×712+16=14828m
= 5.28m
So, position of centre of mass of T- shaped lamina is (xcom,ycom)=(0,5.28)m