A uniform disc of radius R is put over another uniform disc of radius 2R of same thickness and density. The peripheres of the two discs touch each other. The position of their centre of mass is

# A uniform disc of radius R is put over another uniform disc of radius 2R of same thickness and density. The peripheres of the two discs touch each other. The position of their centre of mass is

1. A

at R/3 from the centre of the bigger disc towards the centre of the smaller disc

2. B

at R/5 from the centre of the bigger towards the centre of the smaller disc

3. C

at 2R/5 from the centre of the bigger disc towards the centre of the smaller disc

4. D

none of the above

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### Solution:

for uniform disc, $\mathrm{m}={\mathrm{\pi R}}^{2}\mathrm{d}⇒\mathrm{m}\propto {\mathrm{R}}^{2}$

distance from centre of bigger disc is
${\mathrm{x}}_{2}=\frac{{\mathrm{m}}_{1}\mathrm{d}}{{\mathrm{m}}_{1}+{\mathrm{m}}_{2}}=\frac{{\mathrm{R}}^{2}\left(\mathrm{R}\right)}{{\mathrm{R}}^{2}+4{\mathrm{R}}^{2}}=\frac{{\mathrm{R}}^{2}\left(\mathrm{R}\right)}{5{\mathrm{R}}^{2}}=\frac{\mathrm{R}}{5}$

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