Question

Can a body have kinetic energy without having momentum?

Answer 1

The body has zero momentum signifies that either the body has zero mass or the velocity of a body is zero. If either of the mass or velocity is zero, the kinetic energy (K = $\frac{1}{2}$m$v^2$ ) will be zero. Therefore, it is not possible that a body has kinetic energy without having momentum. Since the photon has zero rest mass, therefore, the kinetic energy of the photon is zero, but still, the photon has momentum. Therefore a body has a momentum without having kinetic energy.