There is a disc of radius R. A small disc is cut from that disc such that the centre of first disc lies on the circumference of the second one. Find out the centre of mass of the remaining disc.

Asked by Anvita Chaudhary | 18th Oct, 2013, 05:43: PM

Expert Answer:

The disc of radius R has mass say M.
Now a disc is cut out such that centre of disc of radius R lies on circumference of the disc that is cut out. Hence, the radius of this disc will be R/2.
 
 
The centre of mass of big disc will be at its centre C. We consider this point as origin. Hence, coordinates of C are (0,0)
The centre of mass of small disc will be at its centre which is a distance R/2 away from C. Hence, coordinates of C1 are (R/2,0).
After the disc is cut, the centre of mass shifts. Let the coordinates of new centre of mass be (x,0).
 
Let the mass per unit area of big disc be m = M/?R2.
 
Thus, mass of the removed part is = M1 = m(?R2/4) = M/4.
Hence, mass of remaining part of disc is M2 = M - M/4 = 3M/4.
 
Thus, the position of centre of mass of whole disc can be written as
 
 
Hence, centre of mass of remaining disc shifts to the left of original centre C.

Answered by Romal Bhansali | 22nd Oct, 2013, 09:41: AM

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