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NTA Abhyas JEE Main2020PhysicsCenter of Mass, Momentum and CollisionPractice

An undeformed spring of spring constant k is connected to a bead of mass m which can move along a frictionless rod as shown in the figure. If the particle strikes the bead at an angle of 45 ° with the horizontal and sticks to it, then the maximum elongation of the spring after the collision is

Options

  1. Av 4 m 2k
  2. Bv 2 m k
  3. Cv 2 m 2k
  4. Dv 4 m k

Correct answer

B. v 2 m k

Step-by-step solution

Conserving the linear momentum of the system along the rod mv cos 45 ∘ = 2 mv 1 v 1 = v 2 2 Applying work-energy theorem - 1 2 kx 2 = - 1 2 2 m v 2 2 2 ⇒   x = v 2 m k

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