Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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Consider the Following Two Statements: (A) Linear Momentum of a System of Particles is Zero. (B) Kinetic Energy of a System of Particles is Zero. - Physics


Consider the following two statements:

(A) Linear momentum of a system of particles is zero.

(B) Kinetic energy of a system of particles is zero.


  • A implies B and B implies A. 

  • A does not imply B and B does not imply A. 

  • A implies B but B does not imply A. 

  • B implies A but A does not imply B. 

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B implies A but A does not imply B. 

If the linear momentum of a system is zero,
\[\Rightarrow m_1 \vec{v}_1 + m_2 \vec{v}_2 + . . .\] =0
Thus, for a system of comprising two particles of same masses,
\[\vec{v}_1 = - \vec{v}_2\]    ...(1)
The kinetic energy of the system is given by,
\[K . E . = \frac{1}{2}m \vec{v}_1^2 + \frac{1}{2}m \vec{v}_2^2\]
Using equation (1) to solve above equation, we can say:
\[K . E . \neq 0\] 

i.e A does not imply B .
If the kinetic energy of the system is zero,
\[\Rightarrow \frac{1}{2}m \vec{v}_1^2 + \frac{1}{2}m \vec{v}_2^2 = 0\]
\[v_1 = \pm v_2\]
On calculating the linear momentum of the system, we get:
\[\vec{P} = m \vec{v}_1 + m \vec{v}_2 \]
\[\text{ taking v_1 = - v_2 , we can write:} \]
\[ \vec{P} = 0\]

Hence, we can say, B implies A but A does not imply B.

Concept: Momentum Conservation and Centre of Mass Motion
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HC Verma Class 11, 12 Concepts of Physics 1
Chapter 9 Centre of Mass, Linear Momentum, Collision
MCQ | Q 3 | Page 157
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