Pertanyaan

Sebuah bola pejal jari-jarinya 4R. Pada bagian dalam bola terdapat rongga bola yang berupa bola dengan jari-jari 2R. Letak titik berat bola tersebut adalah pada x = ....

1/6 R
1/7 R
2/7 R
2/9 R
2/11 R

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Klaim

F. Afrianto

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

Jawaban terverifikasi

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Keterangan :

$begin mathsize 12px style x subscript 1 equals titik space setimbang space bola space besar x subscript 2 equals titik space setimbang space bola space kecil straight x subscript 1 equals 0 straight V subscript 1 equals 4 over 3 πr cubed straight V subscript 1 equals 4 over 3 straight pi open parentheses 4 straight R close parentheses cubed straight V subscript 1 equals fraction numerator 256 straight space πR cubed over denominator 3 end fraction straight x subscript 2 equals negative 2 straight R straight V subscript 2 equals 4 over 3 πr cubed straight V subscript 2 equals 4 over 3 straight pi open parentheses 2 straight R close parentheses cubed straight V subscript 2 equals fraction numerator 32 straight space πR cubed over denominator 3 end fraction straight x subscript 0 equals fraction numerator straight V subscript 1 straight x subscript 1 minus straight V subscript 2 straight x subscript 2 over denominator straight V subscript 1 minus straight V subscript 2 end fraction straight x subscript 0 equals fraction numerator fraction numerator 256 straight space straight pi straight space straight R cubed over denominator 3 end fraction open parentheses 0 close parentheses minus fraction numerator 32 πR cubed over denominator 3 end fraction open parentheses negative 2 straight R close parentheses over denominator fraction numerator 256 straight space πR cubed over denominator 3 end fraction minus fraction numerator 32 straight space πR cubed over denominator 3 end fraction end fraction straight x subscript 0 equals fraction numerator 0 plus 64 straight R over denominator 224 end fraction equals 2 over 7 straight R end style$