Question

a body cannot have kinetic energy without having momentum or vice versa . justify your answer

Answer 1

A single object cannot have momentum without having kinetic energy; if it has a non-zero velocity, it has non-zero kinetic energy. However, several objects can have lots of kinetic energy but no net momentum: momentum is a vector, but energy is a scalar.Yes, a body can have energy without possessing momentum. A body may have potential energy and still can be at rest. This means it would have zero momentum and still it could possess energy. ... A brick placed on the top of a building has a PE = mgh, but has got no momentum because it is not moving.This is not necessarly zero, and thus it is possible to change the kinetic energy of an object without changing its momentum as long as the object's mass is not fixed. If the object's mass is fixed then of course it is quite impossible.

Answer 2

A body cannot have kinetic energy without moving momentum because:

Mass of a body = m

Velocity of a body =v

Momentum of a body = mass x velocity = mv  = p

Kinetic energy = mv²/2

mv*v/2   [∵v²=v*v]

p*v/2 [∵p=mv]

Now as you can see that if momentum (p) will become 0 i.e if body is not showing any momentum then the kinetic energy of the body will become 0.

So  "A body cannot have kinetic energy without having momentum."