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Most Important Selected Qs for JEE AdvancedPhysicsCenter of Mass, Momentum and Collision

Two blocks A and B, each of mass m , are connected by an ideal spring of stiffness k and placed on a smooth horizontal surface. A ball of mass m moving with a velocity v₀ strikes the block A and gets embedded to it. Then,

Options

  1. Avelocity of block A just after collision is v₀ / 2
  2. Bvelocity of block B just after collision is zero
  3. Cthe maximum compression produced in the spring is v₀ m 6 k
  4. Dthe kinetic energy lost during collision is 1 4 m v₀^2

Correct answer

D. the kinetic energy lost during collision is 1 4 m v₀^2

Step-by-step solution

During the collision imples is not transferred to B : m v₀=2 m v^ v^ = v₀ 2 Just after collision v_A= v₀ 2 and v_B=0 and at the time of maximum compression aligned & v_B=m v₀=3 m v^ v^ = v₀ 3 & 1 2 k x₀^2= 1 2 2 m ( v₀ 2 )^2- 1 2 3 m ( v₀ 3 )^2 x₀=v₀ m 6 k & Loss in KE = 1 2 m v₀^2- 1 2 (2 m) ( v₀ 2 )^2= m v₀^2 4 aligned

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