Question

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

• A. True
• B. False

Answer 1

The correct option is A True

1. Consider a system of two particles A and B. Let $m_A$ and $m_B$ be their masses and $v_A$and $v_B$ 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.
   → → → → →
   $P=P_A+P_B=m_A{v}_A+m_B{v}_B$
   $P=m_A{v}_A-m_B{v}_B$
   The total kinetic energy of the particle is,
   $K=K_A+K_B$
   $K=\frac{m{v}_A^2}{2}+\frac{m{v}_B^2}{2}$
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,$m_A{v}_A=m_B{v}_B$. In this situation, even though the momentum is zero, the kinetic energy of the particle is non-zero.
   

Hence, the given statement is True.