Answer to Question #182971 in Mechanics | Relativity for Carley

Question

A metal bowl with a weight of 2.25 N is placed in a larger kitchen container filled with soybean oil. How much soybean oil must the bowl displace in order to float? For reference, the mass density of soybean oil is about 917 g/liter and its weight density is about 8.99 N/liter. Please give your answer in liters.

Answer 1

To be given in question

$F_{g}=mg=2.25N$

$\rho$ _oil =917g/liter

$\rho$ _w=8.99N/liter

To be asked in question

Oil displacement hight (h)=?

We know that

Buoyant force $F_{b}=-{\rho}_{w} g v$

But look at that! The mass of the displaced fluid times the magnitude of the acceleration due to gravity is just the weight of the displaced fluid. So remarkably, we can write the formula for the buoyant force as,

F_b=W

​ W=mg

Magnitude of buoyant force =gravity

$\rho_{w} vg =mg \rightarrow(1)$

Due to Equation (1)we can find out

$v=\frac{mg}{\rho_{w}g}\rightarrow(2)$

Equation (2)put value

$v=\frac{2.25}{8.99} liter$

$v=0.250 liter$