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

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A

$a$

B

2 $a$

C

3 $a$

D

None of these

Solution:

We assume that origin is situated at the $O_{1}$
$∴ \, x_{1}=0,m_{1}=m,$
$x_{2}=3a,m_{2}=2m$
$∴ \, x_{C M}=\frac{m_{1} x_{1} + m_{2} x_{2}}{m_{1} + m_{2}}$
$=\frac{m \times 0 + 2 m \times 3 a}{m + 2 m}$
$=\frac{6 m a}{3 m}=2a$

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