ch14-p037 - 4 3 (0 . 090 m) 3 (0 . 080 m) 3 = 9 . 09 10 4 m...

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Thus m = ρV s . The submerged volume is half the volume enclosed by the outer surface of the sphere, or V s = 1 2 (4 π/ 3) r 3 o , where r o is the outer radius. This means m = 4 π 6 ρr 3 o = ± 4 π 6 ² (800 kg / m 3 )(0 . 090 m) 3 =1 . 2kg . Air in the hollow sphere, if any, has been neglected. (b) The density ρ m of the material, assumed to be uniform, is given by ρ m = m/V , where m is the mass of the sphere and V is its volume. If r i is the inner radius, the volume is V = 4 π 3 ( r 3 o r 3 i ) =
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Unformatted text preview: 4 3 (0 . 090 m) 3 (0 . 080 m) 3 = 9 . 09 10 4 m 3 . The density is = m V = 1 . 22 kg 9 . 09 10 4 m 3 = 1 . 3 10 3 kg / m 3 . 37 (a) The force of gravity mg is balanced by the buoyant force of the liquid gV s : mg = gV s . Here m is the mass of the sphere, is the density of the liquid, and V s is the submerged volume....
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