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:

• A. a
• B. 2a
• C. 3a
• D. None of these

Answer 1

The correct option is B 2a

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 $x=\frac{m_1{x}_1+m_2{x}_2}{m_1+m_2}=\frac{m\times 0+2m\times 3a}{m+2m}=2a$

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