First slide

Location of centre on mass for multiple point masses

Question

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

Easy

A

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

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

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

none of the above

Solution

for uniform disc, $\large m = \pi {R^2}d\,\, \Rightarrow m\propto R^2$
$\large {m_1} \propto {R^2},{m_2} \propto \left( {2R} \right)^2\, \Rightarrow {m_2} \propto 4{R^2}\;d = R$
distance from centre of bigger disc is $\large {x_2} = \frac{{{m_1}d}}{{{m_1} + {m_2}}} = \frac{{{R^2}\left( R \right)}}{{{R^2} + 4{R^2}}} = \frac{{{R^2}\left( R \right)}}{{5{R^2}}} = \frac{R}{5}$

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