The mass of Jupiter is approximately 1.90×10^27 kg. The mass of Earth is approximately 5.97×10^24 kg.

  1. (a)

    Giving your answer in standard form, calculate how many times Jupiter's mass is, compared to that of Earth's.

    Answer ...

  2. (b)

    Density refers to the mass per unit volume.

    Given that the volume of Jupiter is 1.43×10^24 m^3 and that of Earth's is 1.08×10^21 m^3, calculate and determine which planet has a higher density.

    Answer ...

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Worked solution

8(a)

1. Find the ratio of Jupiter's mass to Earth's mass and express it in standard form.

1.90×10275.97×1024=1.905.97×1027−24\frac{1.90\times10^{27}}{5.97\times10^{24}}=\frac{1.90}{5.97}\times10^{27-24}
=0.318257…×103=3.18257…×102=0.318257\ldots\times10^3=3.18257\ldots\times10^2
≈3.18×102\approx 3.18\times10^2

Answer

3.18×1023.18 \times 10^2 times

8(b)

1. Calculate Jupiter's density using mass divided by volume.

Density of Jupiter=1.90×10271.43×1024\text{Density of Jupiter}=\frac{1.90\times 10^{27}}{1.43\times 10^{24}}
=1.328…×103=1.328\ldots\times 10^3
≈1.33×103 kg/m3\approx 1.33\times 10^3\text{ kg/m}^3

2. Calculate Earth's density and compare it with Jupiter's density.

Density of Earth=5.97×10241.08×1021\text{Density of Earth}=\frac{5.97\times 10^{24}}{1.08\times 10^{21}}
=5.527…×103=5.527\ldots\times 10^3
≈5.53×103 kg/m3\approx 5.53\times 10^3\text{ kg/m}^3
Since 5.53×103>1.33×1035.53\times 10^3>1.33\times 10^3, Earth has the higher density.

Answer

Jupiter: 1.33×103 kg/m31.33 \times 10^3\text{ kg/m}^3, Earth: 5.53×103 kg/m35.53 \times 10^3\text{ kg/m}^3. Hence, Earth has a higher density.

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