Question

Consider the following two statements.
(A) Linear momentum of a system of particles is zero.
(B) Kinetic energy of system of particles is zero.

• A. A does not imply B and B does not imply A.
• B. A implies B but B does not imply A
• C. A does not imply B but B implies A
• D. A implies B and B implies A.

Answer 1

The correct option is C A does not imply B but B implies A

Consider a system of two particles.

If linear momentum of the system is zero, this does not implies that momentum of each particle is zero.

Let say the two particles, having equal magnitude of momentum, are moving in opposite direction. Thus magnitude of linear momentum of each particle is a finite quantity i.e. $|p_1|=|p_2|\ne 0$ .

Thus kinetic energy of the system $KE=\frac{|P_1{|}^2}{2m_1}+\frac{|p_2{|}^2}{2m_2}\ne 0$

Hence statement A does not imply B.

If kinetic energy of the system is zero, this implies that momentum of each particle is zero i.e. $p_1=p_2=0$

Thus linear momentum of the system $p=p_1+p_2=0$

Thus statement B implies A.