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NEETPhysicsCenter of Mass, Momentum and Collision

A body of mass m moving along the positive x-axis with speed v collides completely inelastically with another identical body of mass m moving along the positive y-axis with the same speed v . What is the magnitude of the velocity of the combined mass immediately after the collision?

Options

  1. Av
  2. Bv 2
  3. Cv 2
  4. D2 v

Correct answer

C. v 2

Step-by-step solution

The initial momentum of the system is the vector sum of the momenta of the two bodies. Initial momentum vector, p _i = m v i + m v j The magnitude of the initial momentum is: | p _i| = (mv)^2 + (mv)^2 = 2 m v In a completely inelastic collision, the bodies stick together, so the total mass becomes m + m = 2m . Let the final velocity be v _f . Final momentum vector, p _f = (2m) v _f By conservation of linear momentum, p _i = p _f . Therefore, their magnitudes must also be equal: | p _f| = | p _i| (2m) | v _f| = 2 m

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