Review: The true weight of an object can be measured in a vacuum, where buoyant forces are absent. A measurement in air, however, is disturbed by buoyant forces. An object of volume V is weighed in air on an equal-arm balance with the use of counterweights of density $ρ$ . Representing the density of air as $ρ_{a i r}$ and the balance reading as $F_{g}'$ , show that the true weight $F_{g}$ is
$F_{g} = F_{g}' + (v - \frac{F_{g}'}{ρ g}) ρ {}_{a i r}g$

Question

Review: The true weight of an object can be measured in a vacuum, where buoyant forces are absent. A measurement in air, however, is disturbed by buoyant forces. An object of volume V is weighed in air on an equal-arm balance with the use of counterweights of density $ρ$ . Representing the density of air as $ρ_{a i r}$ and the balance reading as $F_{g}'$ , show that the true weight $F_{g}$ is
$F_{g} = F_{g}' + (v - \frac{F_{g}'}{ρ g}) ρ {}_{a i r}g$

Accepted Answer

Hence it is proved that:

$F_{g} = F_{g}' + (v - \frac{F_{g}'}{ρg}) ρ {}_{air}g$

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Identification of the given data

Significance of the buoyant force

Determination of the true weight Fg

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Physics For Scientists & Engineers

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Identification of the given data

Significance of the buoyant force

Determination of the true weight Fg

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