The rest mass of a proton is 1.673 x 10⁻²⁷ kg. At what speed would the mass of the proton be tripled? (Answer: 0.9428c)
Given Data:
Rest mass of the Proton = m₀ = 1.673 x 10⁻²⁷ kg
Relativistic mass of the Proton = m = 3m₀
To Find:
Speed of Proton = v = ?
Solution:
According to special theory of relativity, the observed (increase) mass m is given by
m = m₀√1-v2c2
putting the value of m
3m₀ = m₀√1-v2c2
or
3 = 1√1-v2c2
or (reversing the fraction on both sides
13 = √1-v2c2
Taking square both sides we get
19 = 1 - v2c2
or
v2c2 = 1 - 19
v2c2 = 89
v² = 0.889 c²
taking square root on both sides
v = 0.942 c --------------------Ans.
Thus, when the speed of the proton is 0.942c, its mass increases to triple.
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