Question

an aluminum sphere with a density of 2700kg/m³ is fully submerged in a tank of oil. if the volume of the sphere is 0.025m³, what is the magnitude of the buoyant force acting on the sphere? ? n \\(\
ho_{oil} = 900\\ kg/m³\\)

Explanation:

Step1: Recall Archimedes' Principle

The buoyant force \( F_b \) is given by \( F_b=
ho_{fluid}V_{displaced}g \), where \(
ho_{fluid} \) is the density of the fluid, \( V_{displaced} \) is the volume of the displaced fluid, and \( g = 9.8\ m/s^2 \). Since the sphere is fully submerged, \( V_{displaced}=V_{sphere}=0.025\ m^3 \), and \(
ho_{fluid}=
ho_{oil}=900\ kg/m^3 \).

Step2: Substitute values into the formula

Substitute \(
ho_{oil}=900\ kg/m^3 \), \( V_{displaced}=0.025\ m^3 \), and \( g = 9.8\ m/s^2 \) into the formula:
\( F_b=
ho_{oil}V_{displaced}g = 900\ kg/m^3\times0.025\ m^3\times9.8\ m/s^2 \)

Step3: Calculate the product

First, calculate \( 900\times0.025 = 22.5 \). Then, multiply by \( 9.8 \): \( 22.5\times9.8 = 220.5 \)

Answer:

\( 220.5 \)