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Question

A system of two particles can have non-zero kinetic energy and zero momentum.


A
True
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B
False
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Solution

The correct option is A True
  1. Consider a system of two particles A and B. Let mA and mB be their masses and vAand vB be their velocities. Imagine that the two particles are moving towards each other.
    The total momentum of the particles is the vector sum of the momenta of individual particles.
    → → → → →
    P=PA+PB=mAvA+mBvB
    P=mAvA-mBvB
    The total kinetic energy of the particle is,
    K=KA+KB
    K=mvA22+mvB22
  2. From the above situation, in which the two particles are moving towards each other, the total momentum of the particle is zero, that is,mAvA=mBvB. In this situation, even though the momentum is zero, the kinetic energy of the particle is non-zero.

Hence, the given statement is True.


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