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JEE Advanced2010PhysicsCenter of Mass, Momentum and CollisionActual

A point mass of 1 ~kg collides elastically with a stationary point mass of 5 ~kg . After their collision, the 1 ~kg mass reverses its direction and moves with a speed of 2 ~ms ⁻¹ . Which of the following statement(s) is/are correct for the system of these two masses?

Options

  1. ATotal momentum of the system is 3 ~kg - ms ⁻¹
  2. BMomentum of 5 ~kg mass after collision is 4 ~kg - ms ⁻¹
  3. CKinetic energy of the centre of mass is 0.75 ~J
  4. DTotal kinetic energy of the system is 4 ~J

Correct answer

A. Total momentum of the system is 3 ~kg - ms ⁻¹

Step-by-step solution

aligned & v₁^ = ( m₁-m₅ m₁+m₅ ) v₁+ ( 2 m₅ m₁+m₅ ) v₅ & -2= ( 1-5 1+5 ) v₁+0 ( as v₅=0 ) & v₁=3 ~ms ⁻¹ & v₅^ = ( m₅-m₁ m₁+m₅ ) v₅+ ( 2 m₁ m₁+m₂ ) v₁ & =0+ ( 2 1 6 )(3)=1 ~ms ⁻¹ & P_ CM =P_i=(1)(3) & =3 kg - m s & P₅ ^ =(5)(1)=5 kg - m 5 & K_ CM = P_ CM ^2 2 M_ CM & = 9 2 6 =0.75 ~J & K_ total = 1 2 1 (3)^2 & =4.5 ~J & aligned correct options are (a) and (c).

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