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Center of Mass and Collision question

2005 · Q159
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Center of Mass and Collision question

2005 · Q159

NEETPhysicsCenter of Mass and CollisionMCQ+4 / −1
A bomb of mass 30 kg at rest explodes into two pieces of masses 18 kg and 12 kg. The velocity of 18 kg mass is 6 m s−-−1. The kinetic energy of the other mass is :
  1. A
    324 J
  2. B
    486 J
  3. C
    256 J
  4. D
    524 J
View written solutionFree

Correct answer: B

As per law of conservation of linear momentum

m1v1 + m2v2 = 0

⇒v2=(−m1m2)v1 \Rightarrow {v_2} = \left( { - {{{m_1}} \over {{m_2}}}} \right){v_1}⇒v2​=(−m2​m1​​)v1​

⇒v2=(−1812)6=−9 m/s \Rightarrow {v_2} = \left( { - {{18} \over {12}}} \right)6 = - 9\,m/s⇒v2​=(−1218​)6=−9m/s

Now, kinetic energy of second piece

K.E=12(mv22)K.E = {1 \over 2}\left( {mv_2^2} \right)K.E=21​(mv22​)

=12×12×(−9)2 = {1 \over 2} \times 12 \times {\left( { - 9} \right)^2}=21​×12×(−9)2

∴\therefore∴ K.E = 486 J

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