Solved Numerical Problem No. 19.2 ( Unit-19: Dawn of Modern Physics); HSSC-II (Class-12); Physics (Punjab Curriculum and Text Board, Lahore) With Verified Answers

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. 

Similar Questions:

The rest mass of proton is 1.673 ｘ 10⁻²⁷ kg.  At what speed would be the mass of proton be tripled? (Answer: 0.9428c)

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