Question

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) A implies B and B implies A.
(b) A does not imply B and B does not imply A.
(c) A implies B but B does not imply A.
(d) B implies A but A does not imply B.

Answer 1

(c) A implies B but B does not imply A.

Explanation:

Kinetic energy can be written as

$k = \frac{p^{2}}{2m}$

Where in ,

p- momentum

m- mass

Kinetic Energy Depends on Frame  

Linear momentum is a linear momentum vector quantity of a particle system is zero, does not mean that each particle's momentum is zero.

That is, each particle has momentum but its sum of the vector is zero.

The quantity of kinetic energy is scalar, hence its summation is not zero even if the linear momentum is zero.

If the kinetic energy of the particle system is zero, each particle's kinetic energy is zero.

Maximum linear momentum in this case is zero

The condition linear momentum of a system of particles is zero is applicable to second condition- Kinetic energy of a system of particles is zero.

But the condition Kinetic energy of a system particle is zero wont applicable  to the condition - Linear momentum of a system of particles is zero

Therefore A implies B but B does not imply A

Answer 2

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option C is correct.

(c) A implies B but B does not imply A.