Question

The speed of a fast moving particle, whose total energy is twice the mass energy of the particle at rest, is nearly:
1. 0.89 c
2. 0.86 c
3. 0.87 c
4. 0.88 c

Answer 1

Correct Answer - Option 3 : 0.87 c

Concept:

Rest Energy, E₀ = mc²

where m is mass, c is the speed of light

Total energy, E = γmc²

where, \(\gamma = \frac{1}{{\sqrt {1 - \frac{{{v^2}}}{{{c^2}}}} }}\)

Calculation:

Given:

Total energy, E = 2mc², we can write it as,

γmc2 = 2mc2

γ = 2

From the above equation we have,

\(2 = \frac{1}{{\sqrt {1 - \frac{{{v^2}}}{{{c^2}}}} }}\)

v = 0.866 × c

v = 0.87 c

Hence, the required velocity of the particle is 0.87 c.