PhysicsThree 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

A
2R/3
B
2R
C
5R/3
D
4R/3

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

$x_{cm} = \frac{m_{1} x_{1} + m_{2} x_{2} + m_{3} x_{3}}{m_{1} + m_{2} + m_{3}}$

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

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