Grade 11Mechanics

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?

subrat singh

9 Years agoGrade 11

1 Answer

Manas Shukla

9 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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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?

subrat singh

1 Answer

Manas Shukla

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