(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show that the length contraction deforms a sphere in motion to an oblate rotational ellipsoid whose volume decreases by a factor of γ (gamma)

2. Relevant equations

x=x'/γ v=4∏r^3/3 (volume for sphere) v=4∏(a^2)b/3 (volume for prolate and oblate spheroid)

3. The attempt at a solution

The question is taken fromSpecial relativity for beginnersby Jurgen Freund. Firstly, I am confused as to why the question claims that the sphere would deform into an oblate spheroid rather than a prolate spheroid since length contraction does not contract transversely. Anyway by length contraction, the radius (r) of the sphere would contract by a factor of γ, Therefore:

r=a/γ where a is the equatorial radius and b is the polar radius. By subbing r=a/γ into the formula of sphere, through some algebraic manipulation, I get a spheroid whose radius decreased by a factor of γ^3 instead. How should I go about doing it and where are my errors ?

Please help.

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# Homework Help: On length contraction (Special Relativity)

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