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Perhatikan gambar berikut ini! Diketahui massa Matahari = 2 × 1030 kg, massa Mars = 6,4 × 1024 kg, jarak planet Mars ke Matahari = 2,3 × 108 km, dan jarak titik A ke planet Mars adalah 0,50 × 108 km. Potensial gravitasi di titik A adalah ….

Pertanyaan

Perhatikan gambar berikut ini!

Diketahui massa Matahari = 2 × 1030 kg, massa Mars = 6,4 × 1024 kg, jarak planet Mars ke Matahari = 2,3 × 108 km, dan jarak titik A ke planet Mars adalah 0,50 × 108 km. Potensial gravitasi di titik A adalah ….

  1. -26,7 × 108 J/kg

  2. -14,8 × 108 J/kg

  3. -7,4 × 108 J/kg

  4. -14,8 × 105 J/kg

  5. -7,4 × 105 J/kg

F. Noor

Master Teacher

Jawaban terverifikasi

Pembahasan

Diketahui:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank M end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell blank subscript M a t a h a r i end subscript end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cross times end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 10 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell blank to the power of 30 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank kg end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank M end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell blank subscript m a r s end subscript end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 6 , 4 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cross times end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 10 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell blank to the power of 24 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank kg end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank r end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 2 , 3 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cross times end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 10 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell blank to the power of 8 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank km end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 2 , 3 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cross times end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 10 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell blank to the power of 11 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight m end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank r end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell blank subscript m a r s end subscript end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 0 , 50 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cross times end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 10 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell blank to the power of 8 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank km end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 0 , 5 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cross times end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 10 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell blank to the power of 11 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight m end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank G end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 6 , 67 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cross times end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 10 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell blank to the power of negative 11 end exponent end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank Nm end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell blank squared end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank divided by end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank kg end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell blank squared end cell end table end style 

Ditanya:
Potensial gravitasi di titik A?


Untuk menghitung besar potensial gravitasi pada titik A, maka kita bisa gunakan persamaan berikut ini:

begin mathsize 14px style V equals negative fraction numerator G M over denominator r end fraction end style

Namun, sebelum itu hitung terlebih dahulu jarak titik A ke Matahari, yaitu

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row r equals cell r subscript m a r s end subscript plus r subscript m a t a h a r i end subscript end cell row cell 2 , 3 cross times 10 to the power of 11 end cell equals cell left parenthesis 0 , 5 cross times 10 to the power of 11 right parenthesis plus r subscript m a t a h a r i end subscript end cell row cell r subscript m a t a h a r i end subscript end cell equals cell 1 , 8 cross times 10 to the power of 11 space straight m end cell end table end style  

maka potensial gravitasi di titik A adalah

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell V subscript A end cell equals cell V subscript m a r s end subscript plus V subscript m a t a h a r i end subscript end cell row cell V subscript A end cell equals cell open parentheses negative G M subscript m a r s end subscript over r subscript m a r s end subscript close parentheses plus open parentheses negative G M subscript m a t a h a r i end subscript over r subscript m a t a h a r i end subscript close parentheses end cell row cell V subscript A end cell equals cell negative G open parentheses M subscript m a r s end subscript over r subscript m a r s end subscript plus M subscript m a t a h a r i end subscript over r subscript m a t a h a r i end subscript close parentheses end cell row cell V subscript A end cell equals cell negative 6 , 67 cross times 10 to the power of negative 11 end exponent open parentheses fraction numerator 6 , 4 cross times 10 to the power of 24 over denominator 0 , 5 cross times 10 to the power of 11 end fraction plus fraction numerator 2 cross times 10 to the power of 30 over denominator 1 , 8 cross times 10 to the power of 11 end fraction close parentheses end cell row cell V subscript A end cell equals cell negative 6 , 67 cross times 10 to the power of negative 11 end exponent left parenthesis 1 , 11 cross times 10 to the power of 19 right parenthesis end cell row cell V subscript A end cell equals cell negative 7 comma 4 cross times 10 to the power of 8 space straight J divided by kg end cell end table end style   

Jadi, jawaban yang tepat adalah C.

 

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