A flat circular disk of uniform thickness and radius 5.1 cm has a mass of 48 g.

Question

A flat circular disk of uniform thickness and radius 5.1 cm has a mass of 48 g. Now a circle of half the radius cut out of it. The circumference of this small circle just touches the center and the circumference of the disk.
What is the mass of the circle that was cut out?

What is the mass of the part that remains?

How far is the center of mass of the cut out circle from the center of the original disk?

Use the results you have obtained to find the distance from the center of the original disk to the center of mass of the part of the disk that remains after the circle is cut out.

Explanation / Answer

Radius of disc is =5.1x10-2m

Mass(m)=48g

Mass of disc removed=(m/pir2)x(pixr2/4)

(48/4)=12g

Mass of the remaining disc is Equal to =(48-12)g=36g

New position of center of mass is

Xcom=(m1x1-m2x2)/(m1_m2)

Here m1=48g,m2=12g

X1= initial position of center of mass=0

X2=center of mass of removed part=r/2=5.1/2cm

Xcom=((48x0)-(12x5.1x0.5))/(48-12)

=-0.85cm

The center of mass moved by 0.85 cm to the left of original center of mass

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