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Center of Mass question

2024 · 27 Jan · Shift 1 · Q75
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Center of Mass question

2024 · 27 Jan · Shift 1 · Q75

JEE MainPhysicsCenter of MassMCQ+4 / −1
A body of mass 1000 kg1000 \mathrm{~kg}1000 kg is moving horizontally with a velocity 6 m/s6 \mathrm{~m} / \mathrm{s}6 m/s. If 200 kg200 \mathrm{~kg}200 kg extra mass is added, the final velocity (in m/s\mathrm{m} / \mathrm{s}m/s) is:
  1. A
    6
  2. B
    2
  3. C
    3
  4. D
    5
View written solutionFree

Correct answer: D

  1. Given data

    • Initial mass of body: m1=1000 kgm_1 = 1000\,\text{kg}m1​=1000kg
    • Initial velocity: u=6 m/su = 6\,\text{m/s}u=6m/s
    • Extra mass added: m2=200 kgm_2 = 200\,\text{kg}m2​=200kg
  2. Physical principle used When extra mass is added to a moving body without external horizontal force, horizontal momentum is conserved.

    Initial momentum: pi=m1u=1000×6=6000 kg m/sp_i = m_1 u = 1000 \times 6 = 6000\,\text{kg m/s}pi​=m1​u=1000×6=6000kg m/s

  3. Final mass M=1000+200=1200 kgM = 1000 + 200 = 1200\,\text{kg}M=1000+200=1200kg

  4. Apply conservation of momentum Let final velocity be vvv. pf=Mv=1200vp_f = Mv = 1200vpf​=Mv=1200v

    Since momentum is conserved, 6000=1200v6000 = 1200v6000=1200v

    v=60001200=5 m/sv = \frac{6000}{1200} = 5\,\text{m/s}v=12006000​=5m/s

  5. Check options

    • A: 666 ❌
    • B: 222 ❌
    • C: 333 ❌
    • D: 555 ✅

Therefore, the final velocity is 5 m/s5\,\text{m/s}5m/s.

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