Consider the following two statements
$1.$ Linear momentum of a system of particles is zero
$2.$ Kinetic energy of a system of particles is zeroThen
$1$ implies $2$ and $2$ implies $1$
$1$ does not imply $2$ and $2$ does not imply $1$
$1$ implies $2$ but $2$ does not imply $1$
$1$ does not imply $2$ but $2$ implies $1$
Consider the following two statements
$1.$ Linear momentum of a system of particles is zero
$2.$ Kinetic energy of a system of particles is zeroThen
Because linear momentum is vector quantity where as kinetic energy is a scalar quantity.
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