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Center of Mass and Collision question

2009 · Q158
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Center of Mass and Collision question

2009 · Q158

NEETPhysicsCenter of Mass and CollisionMCQ+4 / −1
An explosion blows a rock into three parts. Two parts go off at right angles to each other. These two are, 1 kg first part moving with a velocity of 12 m s−-−1 and 2 kg second part moving with a velocity 8 m s−-−1. If the third part flies off with a velocity of 4 m s−-−1, its mass would be :
  1. A
    7 kg
  2. B
    17 kg
  3. C
    3 kg
  4. D
    5 kg
View written solutionFree

Correct answer: D

When an explosion breaks a rock, by the law of conservation of momentum, initial momentum is zero and for the three pieces,

AIPMT 2009 Physics - Center of Mass and Collision Question 27 English Explanation

Total momentum of the two pieces 1 kg and 2 kg

=122+162=20 kgms−1 = \sqrt {{{12}^2} + {{16}^2}} = 20\,kgm{s^{ - 1}}=122+162​=20kgms−1

The third piece has the same momentum and in the direction opposite to the resultant of these two momentum.

∴\therefore∴ Momentum of the third piece = 20 kg ms–1
Velocity = 4 ms–1

∴\therefore∴ Mass of the 3rd piece = mvv=204{{mv} \over v} = {{20} \over 4}vmv​=420​ = 5 kg

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