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Bila c = kecepatan cahaya, maka kecepatan yang dip...

Bila c = kecepatan cahaya, maka kecepatan yang diperlukan oleh suatu benda supaya massanya bertambah 25% adalah ....

  1. 0,2 c

  2. 0,3 c

  3. 0,5 c

  4. 0,6 c

  5. 0,8 c

Jawaban:

begin mathsize 14px style straight m subscript straight T equals straight m subscript 0 plus 25 percent sign space straight m subscript 0  straight m subscript straight T equals straight m subscript 0 plus 0 comma 25 space straight m subscript 0  straight m subscript straight T equals 1 comma 25 space straight m subscript 0 end style

Menurut teori relativitas khusus, massa suatu benda dapat mengalami pemampatan apabila benda tersebut atau pengamat relatif bergerak sangat cepat mendekati kecepatan cahaya.

begin mathsize 14px style straight m subscript straight T space equals fraction numerator straight m subscript 0 over denominator square root of 1 minus begin display style straight v squared over straight c squared end style end root end fraction end style

Maka :

begin mathsize 14px style straight m subscript 0 over straight m subscript straight T equals square root of 1 minus straight v squared over straight c squared end root  fraction numerator begin display style straight m subscript 0 end style over denominator begin display style 5 over 4 straight m subscript 0 end style end fraction equals square root of 1 minus fraction numerator begin display style straight v squared end style over denominator begin display style straight c squared end style end fraction end root  open parentheses fraction numerator begin display style 4 space straight m subscript 0 end style over denominator begin display style 5 space straight m subscript 0 end style end fraction close parentheses squared space equals open parentheses square root of 1 minus fraction numerator begin display style straight v squared end style over denominator begin display style straight c squared end style end fraction end root close parentheses squared  16 over 25 equals 1 minus fraction numerator begin display style straight v squared end style over denominator begin display style straight c squared end style end fraction  straight v squared over straight c squared equals 1 minus 16 over 25  square root of straight v squared over straight c squared end root equals square root of 9 over 25 end root  straight v over straight c equals 3 over 5  straight v equals fraction numerator begin display style 3 end style over denominator begin display style 5 end style end fraction straight c  straight v equals space 0 comma 6 space straight c end style

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