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A circular hole of radius 1m. is cut off from a disc of radius 6m.The center of the hole is 3m. from the center of the disc.Find the center of mass of remaining disc.

A circular hole of radius 1m. is cut off from a disc of radius 6m.The center of the hole is 3m. from the center of the disc.Find the center of mass of remaining disc.

Grade:11

1 Answers

Eshan
askIITians Faculty 2095 Points
4 years ago
Dear student,

The disc with hole can be assumed to be a whole disc of radius 6m with its given mass, say M+ a disc of radius 1m whose center is at distance 3m from that of bigger disc and has mass ‘-m’

Since the mass distribution on both of them must be uniform,

\dfrac{M}{\pi (6^2)}=\dfrac{m}{\pi (1^2)}
\implies m=\dfrac{M}{36}
The distance of center of mass of the system from the center of the larger disc will be

\dfrac{M(0)+(-m)(3)}{M+m}=-\dfrac{3}{37}m

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