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Question

# The position of the centre of mass of a uniform bar made up of three rods each having length 2 m and negligible area of cross-section as shown in figure is [Assume masses of the rods are equal]

A
(2 m,2 m)
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B
(23 m,2 m)
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C
(1 m,1 m)
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D
(23 m,1 m)
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Solution

## The correct option is D (23 m,1 m)Let the mass of each rod be m kg Taking the origin at the position shown in figure, (x1,y1)= co-ordinate of COM of rod I = (1,0) (x2,y2)= co-ordinate of COM of rod II = (0,1) (x3,y3)= co-ordinate of COM of rod III = (1,2) x - co-ordinate of COM of system =m1x1+m2x2+m3x3m1+m2+m3 =m(1)+m(0)+m(1)m+m+m=23 m y - co ordinate of COM of system =m1y1+m2y2+m3y3m1+m2+m3 =m(0)+m(1)+m(2)m+m+m =3m3m=1 m ∴(xcom,ycom)=(23 m,1 m)

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