Question

Two small particles of equal masses start moving in opposite directions from a point. A in a horizontal circular orbit. Their tangential velocities are v and 2v, respectively, as shown in the figure. Between collisions, the particles move with constant speeds. After making how many elastic collisions, other than that at A, these two particles will again reach the point A.

 

(A) 1 

(B) 2 

(C) 3 

(D) 4

Answer 1

Correct option: (B) 2

Explanation:

First collision will occur when θ satisfies equation 

{(θ × r) / v} = [{(2π – θ)r} / {2v}]

i.e. θ = π – (θ/2)

(3/2)θ = π

θ = 120°

After first collision at B m₂ will move back with speed V and make second collision with m₁ at C. 

After second collision at C m₁ will move back with speed V and meet m₂ at A. 

if the third collision at A is neglected then 2 collisions are made before they reach A. 

way 2: 

Let particle m₁ is moving in anticlockwise direction and m₂ in clockwise direction. Given is 

{(Vm₁) / (Vm₂)} = (V / 2V) = (1/2) 

hence ratio of distance covered will be 2:1 means they collide at B and C. 

After these two collision particles will meet again at point A.