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A uniform disc of radius R is taken and out of it a disc of diameter R/2 is cut off from end. The center of mass of remaining part will be?

A uniform disc of radius R is taken and out of it a disc of diameter R/2 is cut off from end. The center of mass of remaining part will be?

Grade:11

1 Answers

Manas Shukla
102 Points
7 years ago
Let M be the mass of the full disc , M’ be the mass of the partial disc and m be the mass of the smaller removed disc. If p is the density of the disc materials
Then
M = p\Pi R^{2}
m =\frac{1}{16} p\Pi R^{2}
M` =\frac{15}{16} p\Pi R^{2}
Now Lets assume the centre of whole disc is at origin and thus removed disc centre is at (0,3R/4)
As we see it will be symmetrical along x axis thus centre of mass along y coordinate wont change.
For x coordinate we have
M\times 0 =\frac{1}{16} p\Pi R^{2} \times \frac{3R}{4} + \frac{15}{16} p\Pi R^{2} \times x
x = \frac{-R}{20}
Thus new coordinate for CoM = (0,-R/20)

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