Consider the following two statement:
$I .$ Linear momentum of a system of particles is zero.
$I I .$ Kinetic energy of a system of particles is zero.
Then

I

implies

I I

but

I I

does not imply

I

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I

does not imply

I I

but

I I

implies

I

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I

implies

I I

and

I I

implies

I

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I

does not imply

I I

and

I I

does not imply

I

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Solution

The correct option is B $I$ does not imply $I I$ but $I I$ implies $I$ .
Let's say two bodies of equal masses are in motion with same velocity in opposite direction, then the linear momentum of the system is zero, but the kinetic energy is not zero.
But when kinetic energy of the system of particles is zero, kinetic energy of each has to be zero i.e speed of each particle is zero.. Hence, momentum of the system of particles is zero.
$I$ does not imply $I I$ but $I I$ implies $I$ .

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