What is the mass of a 70kg man in a space rocket traveling at 0.8c from us as measured from Earth?
[Ans. 116.7 kg]



Given:


Rest Mass of man = m₀ = 70 kg

Speed of the rocket relative to the observer on earth = v = 0.8 c 


To Find:

Relativistic mass = m = ?


Solution:


The formula for relativistic mass in the special theory of relativity is given by: 

m = `\frac {m₀}{sqrt {1 - frac {v^2}{c^2}}}`

by putting values

m = `\frac {70 kg}{sqrt {1 - frac {(0.8c)^2}{c^2}}}`

m = `\frac {70 kg}{sqrt {1 - frac {0.64 \cancel {c^2}}{\cancel {c^2}}}}`

c² will be canceled so,

m = `\frac {70 kg}{sqrt {1 - 0.64}}`

m = `\frac {70 kg}{sqrt {0.36}}`


m = `\frac {70 kg}{0.6}`

m = 115.667 kg    -----------------Ans.

Thus, when a man in a rocket traveling in space at speed v = 0.8 c, the relativistic mass of the man is measured as 115.667 kg. 


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