Three identical spheres each of radius ‘R’ are placed touching each other so that their centres A,B and C lie on a straight line. the position of their centre of mass from A is

# Three identical spheres each of radius ‘R’ are placed touching each other so that their centres A,B and C lie on a straight line. the position of their centre of mass from A is

1. A

2R/3

2. B

2R

3. C

5R/3

4. D

4R/3

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### Solution:

The coordinates of the centres of the other two spheres w.r.t the centre of A will be as shown in figure.

Therefore, COM will be at

${\mathrm{x}}_{\mathrm{cm}}=\frac{{\mathrm{m}}_{1}{\mathrm{x}}_{1}+{\mathrm{m}}_{2}{\mathrm{x}}_{2}+{\mathrm{m}}_{3}{\mathrm{x}}_{3}}{{\mathrm{m}}_{1}+{\mathrm{m}}_{2}+{\mathrm{m}}_{3}}$

$=\frac{\mathrm{m}\left(0\right)+\mathrm{m}\left(2\mathrm{R}\right)+\mathrm{m}\left(4\mathrm{R}\right)}{3\mathrm{m}}=\frac{6\mathrm{mR}}{3\mathrm{m}}=2\mathrm{R}$

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