A uniform disc of radius $R$ is put over another uniform disc of radius $2 R$ made of same material having same thickness. The peripheries of the two discs touches each other. Locate the centre of mass of the system taking centre of large disc at origin.

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Solution

$L e t t h e c e n t e r o f b i g g e r d i s c b e O . L e t t h e c e n t e r o f s m a l l e r d i s c b e P . O P = r . m a s s o f t h e s m a l l e r d i s c = m M a s s o f t h e b i g g e r d i s c = 4 m, a s a r e a i s 4 t i m e s . C e n t e r o f m a s s f r o m O : \frac{(4 m \times 0 + m \times r)}{(4 m + m)} = r / 5$

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A uniform disc of radius R is put over another uniform disc of radius 2R made of same material having same thickness. The peripheries of the two discs touches each other. Locate the centre of mass of the system taking centre of large disc at origin.

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