Question

Two homogenous spheres $A$ and $B$ of masses $m$ and $2m$ 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. $3a/2$

Answer 1

Answer: (B)

$2a$

we are taking both $A$ and $B$ on 2-D coordinate system. Now assume that sphere $A$ is on centre and $B$ is in touch with A on X-axis hence the centre of sphere is located at $(3a,0)$.

now location of centre of mass with respect to origin

$r_{cm}=\frac{m_A{r}_A+m_B{r}_B}{m_A+m_B}$

assuming that whole mass is centered at center so

$r_{cm}=\frac{m\times 0+2m\times 3a}{m+2m}=2a$

so the correct answer is $\left(B\right)$