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JEE MainPhysicsCenter of Mass, Momentum and Collision

Two point masses of 4 kg and 6 kg are placed on the x-axis. The 4 kg mass is moved 5 cm in the positive x-direction. If the center of mass of the system is observed to shift by 1 cm in the negative x-direction, what is the required displacement of the 6 kg mass?

Options

  1. A10 cm in the negative x-direction
  2. B5 3 cm in the negative x-direction
  3. C3.5 cm in the negative x-direction
  4. D5 cm in the negative x-direction

Correct answer

D. 5 cm in the negative x-direction

Step-by-step solution

The shift in the center of mass of a system of particles is given by the formula: x_ COM = m₁ x₁ + m₂ x₂ m₁ + m₂ Given values are: m₁ = 4 kg m₂ = 6 kg x₁ = +5 cm (since it is moved in the positive x-direction) x_ COM = -1 cm (since the shift is in the negative x-direction) Substituting the values into the formula: -1 = 4(5) + 6( x₂) 4 + 6 -1 = 20 + 6 x₂ 10 -10 = 20 + 6 x₂ 6 x₂ = -30 x₂ = -5 cm The negative sign indicates that the 6 kg mass must be moved 5 cm in the negative x-direction. Answer: 5 cm in the negative

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