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Question

In the figure shown, a hole of radius 2 cm is made in a semicircular disc of radius 6π at a distance 8 cm from the centre C of the disc. The distance of the centre of mass of this system from point C is: (COM of semicircle of radius r is at distance 4r3π from the base)


A
4 cm
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B
8 cm
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C
6 cm
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D
12 cm
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Solution

The correct option is B 8 cm
Point C is assumed to be the origin.
We know that:
y coordinate of COM of the half disc
y1=4r3π=4×6π3π=8 cm
y coordinate of COM of the hole y2=8 cm
which coincides with y1.

So we can see that there is uniform mass removal in all directions w.r.t original COM. So, no change in the position of centre of mass. It will still be 8 cm.

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