Three balls A, B and C are placed on a smooth horizontal surface. Given that `m_A=m_C=4m_B`. Ball B collides with ball C with an initial velocity v as shown in figure. Find the total number of collisions between the balls. All collisions are elastic.

Options

A. One
B. Two
C. Three
D. Four

Answer

B

Explanation

For collision between B and C
`v_(g) = ((m_(1) - em_(2))/(m_(1) + m_(2)))u_(1) + (m_(2)(1 + e))/((m_(1) + m_(2)) u_(2)`
`= ((m - 4m)/(5m)) v + 0 = -3//5 v`
`v_(C ) = (m_(1)(1 + e))/((m_(1) + m_(2)))u_(1) + ((m_(2) - em_(1))/(m_(1) + m_(2))) v_(2) = (m(1 + 1))/(4m) v + 0 = (v)/(2)`
For collsion between A and B :
`v_(A) = 0 + (m(1 + 1))/(5m) xx ((3v)/(5)) = (6)/(25)v`
`v_(B) = 0 + ((m - 4m)/(5m)) (-(3v)/(5)) = (9v)/(25)`
`:' v_(B) lt v_(C )`
`:'` B will not collide with C
Therfore there will be only two collision.