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GATE 2019 ME (ME2) – Question 39

Engineering Mechanics · Impulse and momentum, energy formulations · 2 marks · Multiple choice

A 3 kg ball moving at 4 m/s makes a perfectly elastic direct central impact with a stationary ball of mass m. Its kinetic energy after impact is 6 J. Find possible values of m.

  1. 1 kg only
  2. 6 kg only
  3. 1 kg, 6 kg
  4. 1 kg, 9 kg

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Show answer and explanation

Correct answer: (D) 1 kg, 9 kg

Explanation

After impact, the 3 kg ball has speed magnitude $\sqrt{2(6)/3}=2$ m/s. Elastic-collision velocity is $v_1=4(3-m)/(3+m)$. Solving for $v_1=+2$ gives $m=1$ kg; $v_1=-2$ gives $m=9$ kg. **D**.