A particle of mass m moving with a speed v hits elastically another particle of mass 2m at rest, on a horizontal smooth circular tube of radius R.

Engineering

Physics

Collision

Question

The time after which the next collision will take place is equal to πR/v

Speed of 2m just after collision will be 2v/3

Speed of m just after collision will be v/3

Velocity of separation just after first collision will be v

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Let the final velocity of 2m and m be V₂ and V₁ respctively.
2mV₂ + mV₁ = mV ......(1)

$e = 1 = \frac{V_{2} - V_{1}}{V}$ ........(2)

$On solving, V_{1} = \frac{- V}{3}, V_{2} = \frac{2 V}{3}$

V_sep = V₂ – V₁ = V

$t = \frac{2 πR}{V_{rel}} = \frac{2 πR}{V}$ .