Question

from a uniform circular disc of mass M and radius r a small circular disc of R/2 is removed in such a way that both have a common tangent find the distance of centre of mass of remaining part from the centre of original disc

Answer 1

The distance of the remaining part is R/6.

Mass of the whole disc = M.

Mass of the disc having area as = πr² = M

Mass of the disc having unit area = M/πR²

Mass of the disc having πR²/4 area = M/πR² × πR²/4 = M/4

Position of centre of mass of the remaining part will be -

R' = mass of the remaining part × R +mass of the cut part × R/2 / The remaining mass

R' = 3MR/4 − MR/8 / 3/4M = 5/6R

Therefore,  

The distance from the tangent point will be

=  R - 5/6R

= R/6.

Answer 2

Answer:

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