When the radius line of circular plate is at 0°, indicating the point A (1,0)
Answers
The problem can be broken into two parts.
The CM of the plate after removing the smaller circular portion can be decomposed into two objects such as:
(i) CM of the circular plate of radius 3R without removing the circular portion of radius R
(ii) CM of the circular portion of radius R which has a negative equivalent mass
Since the system symmetrical about the line joining the two centres, CM will lie on this line.
Taking center of the circle of radius 3R as the origin, CM can be calculated.
The co-ordinate of the CM of the large circle is the origin O.
The co-ordinate of the CM of the smaller circle is 3R−R=2R;
A
1
= Area of the circle of radius 3R=π(3R)
2
,
A
2
=Area of the circle of radius R=π(R)
2
The thickness and density of the circular plates are same every where. Hence, area can be taken instead of mass.
X
cm
=
A
1
−A
2
0×A
1
−2R×A
2
=
π×9R
2
−π×R
2
−2R×πR
2
=−
4
R
;
The CM is to the left of the origin of the circle of radius 3R.
Answer:
radius is 3R ... hope i help u