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Dua bola kecil bermassa 4 kg dan M kg ditelakkan t...

Dua bola kecil bermassa 4 kg dan M kg ditelakkan terpisah sejauh 80 cm. Jika gaya gravitasi nol di suatu titik pada garis hubung antara kedua bola dan berada 20 cm dari bola 4 kg, hitunglah nilai M! 

 

  1. (...) 

  2. (...) 

Jawaban:

Gaya Gravitasi dirumuskan dalam persamaan berikut :

begin mathsize 14px style bold italic F bold space bold equals bold space bold italic G bold space fraction numerator bold italic m subscript bold 1 bold space bold italic m subscript bold 2 over denominator bold italic r to the power of bold 2 end fraction end style 

Berdasarkan pada soal, besar gaya gravitasi  di suatu titik pada garis hubung kedua bola adalah Nol. Maka besar begin mathsize 14px style bold italic F subscript bold 1 bold space bold minus bold space bold italic F subscript bold 2 bold space bold equals bold space bold 0 end style, sehingga perhitungan yang didapatkan yaitu :

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell bold italic F subscript bold 1 bold space bold minus bold space bold italic F subscript bold 2 bold space end cell bold equals cell bold space bold 0 end cell row cell bold italic G bold space fraction numerator bold italic m subscript bold 1 bold space bold italic m subscript bold 2 over denominator bold italic r subscript bold 1 to the power of bold 2 end fraction bold space bold minus bold space bold italic G bold space fraction numerator bold italic m subscript bold 2 bold space bold italic m subscript bold 3 over denominator bold italic r subscript bold 2 to the power of bold 2 end fraction bold space end cell bold equals cell bold space bold 0 end cell row cell G space fraction numerator m subscript 1 space m subscript 2 over denominator r subscript 1 squared end fraction space end cell equals cell space G space fraction numerator m subscript 2 space m subscript 3 over denominator r subscript 2 squared end fraction end cell row cell fraction numerator m subscript 1 space m subscript 2 over denominator r subscript 1 squared end fraction space end cell equals cell space fraction numerator m subscript 2 space m subscript 3 over denominator r subscript 2 squared end fraction end cell row cell fraction numerator 4 space kg space times space straight m over denominator open parentheses 0 comma 2 space straight m close parentheses squared end fraction space end cell equals cell space fraction numerator straight m space times space straight M over denominator open parentheses 0 comma 6 space straight m close parentheses squared end fraction end cell row cell fraction numerator 4 space kg over denominator 0 comma 04 space straight m squared end fraction space end cell equals cell space fraction numerator straight M over denominator 0 comma 36 space straight m squared end fraction end cell row cell straight M space end cell equals cell space fraction numerator 4 space kg space cross times space 0 comma 36 space straight m squared over denominator 0 comma 04 space straight m squared end fraction end cell row cell bold M bold space end cell bold equals cell bold space bold 36 bold space bold kg end cell end table end style   

Jadi, besarnya nilai M adalah 36 kg.

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