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JEE MainPhysicsCenter of Mass, Momentum and Collision

A plank of mass 60 kg and length 8 m rests on a frictionless horizontal ice surface. Person P of mass 60 kg stands at the left end of the plank, and Person Q of mass 40 kg stands at the right end. If they walk towards each other and exchange their positions, what is the distance and direction the plank moves relative to the ice?

Options

  1. A1 m towards the left
  2. B1 m towards the right
  3. C1.6 m towards the left
  4. D1.6 m towards the right

Correct answer

A. 1 m towards the left

Step-by-step solution

Since there is no net external horizontal force acting on the system (plank + persons), the center of mass of the system remains stationary. Therefore, x_ COM = 0 . Let the displacement of the plank relative to the ice be x (taking rightwards as positive). Person P moves from the left end to the right end of the plank. The displacement of P relative to the plank is +8 m . The absolute displacement of P relative to the ice is x_P = 8 + x . Person Q moves from the right end to the left end of the plank. The displacem

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