Question

Can a body possess K.E without having momentum? (Yes/ No)

Answer 1

As the question states $\text{a}$ body not a system of bodies.

A body can have only one velocity at a time,

So there is no chance of nullification of velocity by vector addition.

And |velocity| = speed

Hence a body with a non- zero speed (i.e KE) will surely have momentum,

So a body cannot possess speed or KE without momentum.

Answer NO.