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Perbandingan dilatasi waktu untuk sistem yang berg...

Perbandingan dilatasi waktu untuk sistem yang bergerak pada kecepatan 0,8c dengan sistem yang bergerak dengan kecepatan 0,6c adalah ....space

  1. 3 : 4undefined

  2. 4 : 3undefined

  3. 9 : 2undefined

  4. 9 : 16undefined

  5. 16 : 9undefined

Jawaban:

Diketahui:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell v subscript 1 end cell equals cell 0 comma 8 c end cell row cell v subscript 2 end cell equals cell 0 comma 6 c end cell end table end style 

Ditanyakan:

begin mathsize 14px style fraction numerator increment t subscript 1 over denominator increment t subscript 2 end fraction equals ? end style 

Jawab:

Persamaan dilasi/dilatasi waktu:

begin mathsize 14px style increment t equals fraction numerator increment t subscript 0 over denominator square root of 1 minus begin display style v squared over c squared end style end root end fraction end style 

Misalkan begin mathsize 14px style increment t subscript 0 end style bernilai tetap. Perbandingan dilatasi waktu antara sistem 1 dan 2 adalah:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator increment t subscript 1 over denominator increment t subscript 2 end fraction end cell equals cell fraction numerator begin display style bevelled fraction numerator down diagonal strike increment t subscript 0 end strike over denominator square root of 1 minus begin display style v subscript 1 squared over c squared end style end root end fraction end style over denominator begin display style bevelled fraction numerator down diagonal strike increment t subscript 0 end strike over denominator square root of 1 minus begin display style v subscript 2 squared over c squared end style end root end fraction end style end fraction equals fraction numerator square root of 1 minus begin display style v subscript 2 squared over c squared end style end root over denominator square root of 1 minus begin display style v subscript 1 squared over c squared end style end root end fraction end cell row blank equals cell fraction numerator square root of 1 minus begin display style open parentheses 0 comma 6 c close parentheses squared over c squared end style end root over denominator square root of 1 minus begin display style open parentheses 0 comma 8 c close parentheses squared over c squared end style end root end fraction equals fraction numerator square root of 1 minus begin display style fraction numerator 0 comma 36 up diagonal strike c squared end strike over denominator up diagonal strike c squared end strike end fraction end style end root over denominator square root of 1 minus begin display style fraction numerator 0 comma 64 up diagonal strike c squared end strike over denominator up diagonal strike c squared end strike end fraction end style end root end fraction end cell row cell fraction numerator increment t subscript 1 over denominator increment t subscript 2 end fraction end cell equals cell fraction numerator square root of 0 comma 64 end root over denominator square root of 0 comma 36 end root end fraction equals fraction numerator 0 comma 8 over denominator 0 comma 6 end fraction equals bold 4 over bold 3 end cell end table end style 

Dengan demikian, perbandingan dilatasi waktu antara sistem 1 dan 2 adalah 4 : 3.

Jadi, jawaban yang benar adalah B.

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