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JEE Main2017PhysicsCenter of Mass, Momentum and CollisionActual

Two particles A and B of equal mass M are moving with the same speed v as shown in figure. They collide completely inelastic and move as a single particle C . The angle θ that the path of C makes with the X -axis is given by-

Options

  1. Atan ⁡ θ = 3 -   2 1 -   2
  2. Btan ⁡ θ = 1 -   2 2   1 +   3
  3. Ctan ⁡ θ = 1 -   3 1 +   2
  4. Dtan ⁡ θ = 3 +   2 1 -   2

Correct answer

D. tan ⁡ θ = 3 +   2 1 -   2

Step-by-step solution

After inelastic collision mass of the combination is 2m v ' be the velocity of the combined mass Using conservation of momentum along X and Y -axis 2 m v ′ sin ⁡ θ = m v 2 + m v 3 2 2 m v ′ cos ⁡ θ = m v 2 - m v 2 2 sinθ 2 cosθ = 1 2 + 3 2 1 2 - 1 2 = 2 + 3 1 - 2      tan   θ = 2 + 3   1 -   2

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