Two uniform non conducting balls `A and B` have identical size having radius `R` but made of different density material (density of A = 2 density of B). The ball `A is + vely` charged and ball `B` is - vely charged. The balls are released on the horizontal smooth surface at the separation `10 R` as shown in figure. because of mutual attraction the balls start moving towards each other. They will collide at a point.
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Options

A. `x = (10 R)/(3)`
B. `x = (11 R)/(3)`
C. `x = 5 R`
D. `x =(7 R)/(3)`

Answer

A

Explanation

(a) There is no external force on system (ball `A` and ball `B`). The balls moves due to mutual attraction that is internal force to the system. The centre of mass of the system will not move. The will collide at the position of centre of mass is ball `A` and `B` It is easy to calculate the position of centre of mass at initial stage.
`x_(cm) (m_A xx A + m_B xx B)/(m_A + m_B) =(m_A.0 + m_B. 10 R)/((m_A + m_B))`
`m_A = (4)/(3) pi R^2 rho_A` and `m_B = (4)/(3) pi R^3 rho_B`
As `rho_A = 2_ rho B rArr m_A = 2 m_B`
Hence `x_(cm) = (m_B(10 R))/(2 m_B) = (10)/(3) R`.
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