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Verify that a $2.3 \times 10^{17}$ kg mass of water at normal density would make a cube 60 $\mathrm{km}$ on a side, as claimed in Example $31.1 .$ (This mass at nuclear density would make a cube 1.0 $\mathrm{m}$ on a side.

The density of water is $\rho=1000 \mathrm{kg} / \mathrm{m}^{3}$Mass of the water is $m=2.3 \times 10^{17} \mathrm{kg}$Hence, the volume of the water is$$V=\frac{m}{\rho}=\frac{2.3 \times 10^{17} \mathrm{kg}}{1000 \mathrm{kg} / \mathrm{m}^{3}}=2.3 \times 10^{14} \mathrm{m}^{3}$$Hence, the side of the cube have this volume is$$\ell=\sqrt[3]{V}=\sqrt[3]{2.3 \times 10^{14} \mathrm{m}^{3}}=6.13 \times 10^{4} \mathrm{m}=61 \mathrm{km}$$Hence, the side of the cube will be approximately $60 \mathrm{km} .$

Physics 103

Chapter 31

Radioactivity and Nuclear Physics

Nuclear Physics

University of Washington

Simon Fraser University

Hope College

McMaster University

Lectures

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In physics, wave optics is…

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Interference is a phenomen…

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Find the length of a side …

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A cube has a density of $2…

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Ah, the dent steal water role is equal to 1000 kilogram cubic meter. This is the dense deal for her and muscle water. Em m is, uh, most of the water M is equal to 2.3. Multiply by 10 to the power 17 kilogram and aah! Wantem off the water is given by we is equal to mass divided by intensity m divided by rule we have MM mass. It's equal to 2.3. Multiply by 10 to the power 17 kilogram divided by density. Condensed equals 1000 kilograms or a cubic meter, and therefore, volume off the water is equal to 2.3. Multiply by 10 to the power for dean cubic meter, the volume off the water and, uh, the side of the cube. I have this volume is given by ah, we know that volume equals out to the powertrain. Uh, where l is the length off the side of the cube on dhe l equals l equals, um, Cube Rudolph Week on dhe Excuse us. L equals to Louise 2.3. Multiply by 10 to the power 14. 14 cubic meter and l equals 6.13 Multiply by 10 to the power for meters and is equal to 61 kilometers hence. The side of the cube will be approximately so. It's approximately, um equal. Do 60 kilometers, say approximate.

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