Question

A particle having zero rest mass and non- zero energy and momentum must travel with a speed:
A) Equal to c the speed of light in vacuum
B) Tending to infinity
C) Greater than c
D) Less than c

Answer 1

In the given question we have to find the speed of a particle having zero rest mass and non- zero energy and momentum. For this we are going to use the formula of rest mass of a moving particle.

Complete answer:
Given,
The particle has zero rest mass and the energy and momentum of the particle are non- zero. Let v is the speed of the particle; c is speed of light; m is the mass of the particle when it is moving and ${m_ 0}$ is the rest mass of the particle.
As we know that the mass of a moving particle is given by following formula,
$m = \dfrac{{{m_ 0}}}{{\sqrt {1 - \dfrac{{{v^2}}}{{{c^2}}}} }}$….. (1)
Since it is given that the rest mass of the particle is zero, so ${m_ 0} = 0$. Putting the value of ${m_ 0}$ in equation (1) we get;
$\Rightarrow \sqrt {1 - \dfrac{{{v^2}}}{{{c^2}}}} = 0$
Squaring both the side of above equation;
$\Rightarrow 1 - \dfrac{{{v^2}}}{{{c^2}}} = 0$
$\Rightarrow \dfrac{{{v^2}}}{{{c^2}}} = 1$
$\Rightarrow {v^2} = {c^2}$
$\Rightarrow v = c$
It shows that the speed of the particle is equal to the speed of light.
Hence from the above explanation we have seen that the speed of the particle is equal to the speed of light.

So option (A) is correct.

Note: In such types of questions we have to be careful about the conditions given. The example of a given condition is a photon as it has zero rest mass and has non zero energy and momentum and it travels with the speed of light c. Invariant mass is another name for the rest mass of the particles. There is always energy with mass. The rest mass energy of a particle is that energy which is stored in a stationary particle as a result of its mass.