A circular hole of a Radius R/4 is cut from a circular thin uniform disk of mass

Question

A circular hole of a Radius R/4 is cut from a circular thin uniform disk of mass M and radius R. The center of the hole is located at x=r/2 and y=0. Find the center of mass of the object, expressing your answer in terms of M and R.

and oxygen radius R/4 is cut from a the 97. ..Calc A circular hole of radius R. e center of thin, uniform disk of mass M and 0 as shown in the hole is located at R/2 and Figure 7-35. Find the center of mass of the resulting object, expressing your answer in terms of and Figure 7-35 Problem 97

Explanation / Answer

Here, for the mass of the smaller disk

m = M * pi * (R/4)^2/(pi * R^2)

m = M/16

NOw, for the centre of mass

as the centre of mass will lie on x axis due to symmetry

Xcom = (M * 0 - M/16 * R/2)/(M - M/16)

Xcom = - R/30

the centre of mass is located at x = - R/30 , y = 0

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