Question

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

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

Answer: (C)

A does not imply B but B implies A

Since linear momentum of a particle is a vector quantity. The total momentum of a system of two particle of same mass moving opposite to each other with same velocity will be zero. But still it will have kinetic energy.

But if kinetic energy is zero this means that the total system is in rest that readily implies zero linear momentum.

So, A ( Linear Momentum of a system of particles is Zero) does not imply B(Kinetic energy of a system of particles is zero) but B definitely implies A.

Option C