If your average density is $\rho$ and you are floating gently in freshwater with density $1000kg/m^3$, what fraction of your volume will be submerged?

• A. $\frac{\rho }{1000}$
• B. $\frac{1}{\rho }$
• C. $\frac{\rho }{1}$
• D. $\frac{1000}{\rho }$

Answer: (A)

Verified step by step guidance

1. Understand that when an object floats in a fluid, the buoyant force equals the weight of the object. The buoyant force depends on the volume of fluid displaced.
2. Let the total volume of the object be \(V\) and the submerged volume be \(V_{sub}\). The density of the fluid is \(1000\ \text{kg/m}^3\) and the average density of the object is \(\rho\).
3. The weight of the object is \(\rho V g\), where \(g\) is the acceleration due to gravity. The buoyant force is \(1000 \times V_{sub} \times g\).
4. Set the buoyant force equal to the weight to find the submerged volume: \(1000 \times V_{sub} \times g = \rho V g\).
5. Cancel \(g\) from both sides and solve for the fraction submerged: \(\frac{V_{sub}}{V} = \frac{\rho}{1000}\).