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 =  ? 




Solution:


According to special theory of relativity, the observed (increase) mass m is given by

m = m1-v2c2   

putting the value of m

3m₀ = m1-v2c2 

or

3 = 11-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

v² = 0.889c²

v = 0.942 c --------------------Ans.

Thus, when the speed of the proton is 0.942c, its mass increases to triple.



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