Question

Two homogeneous spheres A and B masses m and 2 m having radii 2a and a respectively are placed in touch. The distance of centre of mass from first sphere is
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Answer 1

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Taking the first sphere as the origin and the line joining the centers as x  axis we get, first sphere at (0,0) and the second sphere at (2a+a,0) or at (3a,0)(externally touching so radius added)

so the center of mass will be at

x=  m₁x₁ + m₂x₂ / m₁ + m₂

x = m × 0 + 2m × 3a / m + 2m

x = 2 a

i.e at a distance 2a from the first sphere.

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