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Question

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


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Solution

Step 1. Given data:

Rest mass m0=0

Let v= speed of the particle;

c= speed of light;

m= mass of the particle when it is moving

Step 2. Formula used:

As we know that the mass of a moving particle is given by the following formula,

m=m01-v2c2, where all the variables are described above.

Step 3. Explanation:

Since it is given that the rest mass of the particle is zero, so m0=0. Putting the value of m0 in equation, we get

1-v2c2=0, squaring both sides, we get

1-v2c2=0orv2c2=1v=c

It shows that the speed of the particle is equal to the speed of light.

Particle is a photon and it travels with a velocity equal to light in vacuum.

Hence, a particle that has zero rest mass and non-zero energy and momentum must travel with a speed equal to the speed of light.


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