Question

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

Answer 1

An object's kinetic energy is the energy it possesses due to its motion. It is defined as the work needed to accelerate from rest to the specified velocity of a body of a given mass. Having gained this energy during its acceleration, unless its speed changes, the body maintains this kinetic energy. When a body of mass $\mathrm{m}$ is in motion, it possesses an energy called kinetic energy given as $\dfrac{1}{2}m{{v}^{2}}$where $\mathrm{v}$ is the velocity of the body. The momentum of the body is the product of its mass and its velocity i.e. $\mathrm{p}=\mathrm{mv}$.
Formula used:
$E=\dfrac{1}{2} m v^{2}$
$p=m v$
(m)= mass of the body
(v)= velocity of the body

Complete answer:
1.Momentum of a body is the product of its mass and its velocity. Suppose a body of mass $\mathrm{m}$ is moving with a velocity of $\mathrm{v}$.
2.Then its momentum (p) is given as $\mathrm{p}=\mathrm{mv}$. Momentum is a vector quantity. Its magnitude is the same and its orientation is in the direction of the body's velocity.
3.The body's energy is the sum of work conducted on the body.
4.Mechanical energy is the most universal form of energy. Kinetic energy and potential energy are composed of mechanical energy.
5.The energy possessed by a body while it is in motion is kinetic energy. It depends on the body mass and the square of its velocity. Hence, kinetic energy of a body is given as $\dfrac{1}{2} m v^{2},$ where $m$ is mass of the body and $v$ is velocity of the body.
6.A body's potential energy is the amount of work performed by an external force to bring a body from infinity into a field in which another force affects the body. The term for potential energy relies on the field force that acts on it. Now, if we are considering a body's kinetic energy.
$\therefore$ A body cannot possess speed or KE without momentum.

Answer is no.

Note:
Momentum tells us about the force required to stop a body moving in a given amount of time with a velocity of $\mathrm{v}$. The greater the value of the body's momentum, the greater the amount of force that is needed to stop the body. Larger momentum also indicates more body-possessed energy. Therefore, to bring it to rest, there is more work to be done on the body.