Question

Can a body have energy without having momentum? Why?

Answer 1

No a body has kinetic energy without having momentum. Yes a body has momentum without having kinetic energy. Momentum of a body (p) is defined as the mass of the body (m) time’s velocity of the body (v). p = mv …… (1) Kinetic energy of the body (K) is defined as the, K = ½ mv² …… (2) Where m is the mass of the body and v is the velocity of the body. The body having zero momentum signifies that, either the body has zero mass or the velocity of body is zero. If either of the mass or velocity is zero, then kinetic energy (K = ½ mv²) will be zero. Therefore it is not possible a body has kinetic energy without having momentum. The momentum (p) of photon which has zero rest mass of electromagnetic radiation with wavelength λ is, p = h/λ …… (3) Where h is the Planck’s constant. 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