From a uniform disk of radius R, a circular hole of radius R/2 is cut out. The centre of the hole is at R/2 from the centre of the original disc.Locate the centre of gravity of the resulting flat body.
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Solution
If the mass per unit area of the disc is m,
then mass of the portion remove from the disc is M′=π(R/2)2×m=(πR2/4)m=M/4
In figure centre of mass of M is at O and for M′ is at O′
But OO′=R/2.
After mass M′ is removed the remaining portion can be taken as two masses M at O and −M′=−M/4 at O′ we taking −M′ because we are removing this mass.
distance of centre of gravity(P) of remaining part is :