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.
Text Solution
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number of collisions = 2
Sol.
For B.C.
mv + 0 = mv B + 4mv C
v = v B + 4v C ......(i)
v C – v B = v ......(ii)
(i) + (ii) ⇒ 2v = 5v C ⇒ v C = 
v
v B = v C – v = 
v – v = – 
Now 
– mv B = – 4 mv A – mv B2
v B = 4v A + v B2
v A –v B2 = v B ......(iv)
2v B = 5v A ∴ v A = 
v A = – 
and v B0 = v A – v B
v B2 = 
+ 
= 
v B2 = 
Now again
> 
so B/C will not collide
so no of collision = 2.
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