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Two homogeneous spheres A and B of masses \(m\) and \(2m\), having radii \(2a\) and \(a\) respectively, are placed in contact. The distance of the centre of mass from the first sphere is:

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

Correct answer: 2a

Solution

The centres of the spheres are separated by \(2a+a=3a\). Taking the centre of sphere A as origin, the centre of mass is at \(x=\frac{2m\cdot 3a}{m+2m}=2a\) from A.

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