Question

Is it possible for the momentum of an object to be mc. If not. why not? If so, under what condition?

Short answer

The momentum cannot be mc for objects that have non-zero rest mass. The momentum can be equal to mc only for photons.

Step-by-step solution

Relativistic Momentum

The momentum of a particle moving at speeds, comparable to the speed of light, is called the relativistic momentum. The relativistic momentum of a particle cannot be calculated by using the classical formula of momentum. Relativistic correction is needed to get an accurate answer.

Condition for the possibility of momentum not to be equal to mc

The momentum of a particle is given as:

$p=\frac{E}{c}$

Here, c is the speed of light in a vacuum, are the rest energy of the particle and its value is $m{c}^2$

The particle consists of energy equal to $m{c}^2$ only for rest position of the particle. The energy of the particle moving at relativistic speeds is not equal to $m{c}^2$. At relativistic speeds, the rest mass of the particle gets converted into dynamic mass whose value increases with the increase in velocity. Due to the large mass the dissipation of energy also increases because of the frictional effects. So, particles cannot achieve a speed equal to the speed of light. Hence, the momentum of the particle cannot be mc.

Condition for the possibility of momentum to be equal to mc

The photons are particles with zero rest mass that move at the speed of light. There is no loss of speed due to frictional effects as there is no rest mass. So, the momentum of photons can be equal to mc.