A point mass of 1kg collides elastically with a stationary point mass of 5kg. After their collision, the 1kg 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?

Engineering

Physics

Center of Mass

Collision

Question

A point mass of 1kg collides elastically with a stationary point mass of 5kg. After their collision, the 1kg 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?

Total kinetic energy of the system is 4J

Total momentum of the system is 3kg ms^–1

Kinetic energy of the centre of mass is 0.75 J

Momentum of 5kg mass after collision is 4kg ms^–1

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v = 5v₂ – 2 (1)

v = v₂ + 92

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2v = 6 v₂

v₂ = v/3

v = 5v/3 – 2

–2v / 3 = – 2

v = 3 m/s

v₂ = 1 m/s

$∴$ P_i = 3 kgms^–1

^{$k_{cm} = \frac{1}{2} (1 + 5) v_{cm}^{2} = 3 v_{cm}^{2}$}

^{$v_{cm} = \frac{1 \times 3}{1 + 5} = \frac{1}{2} \Rightarrow km = \frac{3}{4} = 0 .75$}