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Two uniform solid spheres A and B have masses $m$ and $2m$ and radii $2a$ and $a$, respectively. They are placed just touching each other. How far is the centre of mass of the system from the centre of sphere A?

1. $a$
2. $2a$
3. $3a$
4. none of these

Correct answer: $2a$

Solution

The distance between the centres is $2a+a=3a$. Taking the centre of sphere A as origin, sphere B is at $3a$. Then $x_{cm}=\frac{m\cdot 0+2m\cdot 3a}{m+2m}=2a$.

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