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# A particle which has zero rest mass and non-zero energy and momentum must travel with a speed ?

Last updated date: 15th Jul 2024
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Hint:Use the relation between inertial mass and rest mass and apply the given conditions accordingly. Or, try to recall which particle has zero rest mass and non-zero energy and momentum. Rest mass is the mass of a body as measured when the body is at rest. It is a scalar quantity.

Complete step by step answer:
First let us discuss something about given entities
Rest mass: It is the mass of a body as measured when the body is at rest. It is a scalar quantity
Energy: It is the sum of kinetic and potential energy of the particle. It is a scalar quantity.
Momentum: In simple words it is the product of mass of particle and velocity of the particle. It is a vector quantity, i.e., having both magnitude and direction.

We know that $m$ (inertial mass) is related to the ${{m}_{o}}$(rest mass) as following
$m=\dfrac{{{m}_{o}}}{\sqrt{1-\dfrac{{{v}^{2}}}{{{c}^{2}}}}}$
where $v$ is the speed of particles and $c$ is the speed of light.
We have to solve the above equation. Now it is given that the rest mass of the particle is zero. Inertial mass cannot be zero. So the other term should be zero substituting ${{m}_{0}}=0$, we get
$\sqrt{1-\dfrac{{{v}^{2}}}{{{c}^{2}}}}=0$
This gives us that, $v=c$,

Therefore, we get to know that the speed of the particle is the same as the speed of light which means it travels at the same speed as the light.

Note:We get the speed of the particle the same as the speed of light. The particle is a photon. Note that we have directly solved the question if we know the particle as said in the hint given above. The photon is an electromagnetic particle which travels at the speed of light.