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Question

Two discs of radii 5 m and 3 m are joined together along their circumference as shown in the figure below. Find the centre of mass of the system of two discs


A
(6,0) m
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B
(5,0) m
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C
(7,0) m
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D
(4,0) m
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Solution

The correct option is C (7,0) m
Given, m1=3 kg and m2=1 kg


Coordinates of COM of disc 1, (x1,y1)=(5,0) m
Coordinates of COM of disc 2, (x2,y2)=(13,0) m

x- coordinate of COM of the system is given by
xcom=m1x1+m2x2m1+m2
=3×5+1×133+1=284 m=7 m
xcom=7 m

Both discs are symmetric about x - axis. So, y coordinate of COM of the system is zero
So, centre of mass of the system of two discs is at (7,0) m

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