   Chapter 9, Problem 17P

Chapter
Section
Textbook Problem

Buoyant Forces and Archimedes’ PrincipleA table-tennis ball has a diameter of 3.80 cm and average density of 0.084 0 g/cm3. What force is required to hold it completely submerged under water?

To determine
The force required to hold the table-tennis ball completely submerged under water.

Explanation
The following forces involved for the complete submerge of the table-tennis ball are downward gravitational force, downward applied force, and the force of buoyancy they would be written as Fy=F+Bmg=0=mgB . Mass of water is m=ρballV=ρball(4πr3/3) and the buoyancy force is B=ρwaterVg=ρwater(4πr3/3)g .

Using these expressions in the expression of sum forces , the required force to hold the ball is calculated.

Given info: Density of ball is 0.084×103kg/m3 , density of water is 103kg/m3 , radius of the ball is (0.038m)/2 , and acceleration due to gravity is 9.80m/s2 .

The formula for the force required to hold the table-tennis ball submerged under water is,

F=(ρballρwater)(43πr3)g

• ρball is density of the ball.
• ρwater is density of water

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