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MHT CET202013 Oct 2020Morning ShiftPhysicsCenter of Mass, Momentum and CollisionActual

In a system of two particles of masses ' m ₁ ' and ' m ₂ ', the second particle is moved by a distance 'd' towards the centre of mass. To keep the centre of mass unchanged, the first particle will have to be moved by a distance

Options

  1. Am ₁ ~m ₂ d, towards the centre of mass.
  2. Bm ₂ ~m ~d , away from the the centre of mass. m
  3. Cm ₂ ~m ₁ ~d , towards the centre of mass.
  4. Dm ₁ ~m ₂ ~d , away from the centre of mass.

Correct answer

C. m ₂ ~m ₁ ~d , towards the centre of mass.

Step-by-step solution

Correct option is E) given masses are m ₁ and m ₂ let x and y be the distance of m₁ and m₂ from the centre of mass respectively, then m ₁ x = m ₂ y If the mass m₁ is moved by a distance d₁ , and mass m₂ be moved by a distance d ₂ , then m ₁ ( x - d ₁ )= m ₂ ( y - d ₂ ) m ₁ x - m ₁ ~d ₁= m ₂ y - m ₂ ~d ₂ m ₁ ~d ₁= m ₂ ~d ₂ d ₂= m ₁ ~m ₂ ~d ₁ ( constants ) d ₂= m ₁ ~m ₂ ~d ( d ₁= d )

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