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JEE Main201911 Jan 2019Morning ShiftPhysicsCenter of Mass, Momentum and CollisionActual

A body of mass 1 ~kg falls freely from a height of 100 ~m , on a platform of mass 3 ~kg which is mounted on a spring having spring constant k =1.25 10⁶ ~N / m . The bodysticks to the platform and the spring's maximum compression is found to be x . Given that g=10 ~ms ⁻², the value of x will be close to :

Options

  1. A40 ~cm
  2. B4 ~cm
  3. C80 ~cm
  4. D8 ~cm

Correct answer

B. 4 ~cm

Step-by-step solution

Velocity of 1 ~kg block just before it collides with 3 ~kg block = 2 gh = 2000 ~m / s Using principle of conservation of linear momentum just before and just after collision, we get 1 2000 =4 v v = 2000 4 ~m / s Initial compression of spring 1.25 10⁶ x ₀=30 x ₀ 0 using work energy theorem, W _ g + W _ sp = KE 40 x+ 1 2 1.25 10⁶ (0²-x² )=0- 1 2 4 v² solving x 4 ~cm

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