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Density of a floating sphere

  • Thread starter throneoo
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  • #1
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1. Homework Statement
a sphere of uniform density and radius R is floating on water , partially immersed such that the distance between the top of the sphere and the water surface is R/2
find the density of the sphere
2. Homework Equations
Archimedes Principle

3. The Attempt at a Solution
One can deduce from the Archimedes Principle ,that the weight of the displaced water = the weight of the object

ρWaterVDisplaced waterg=ρObject VObjectg

which basically turns the problem into a mathematical problem involving finding the volume of the immersed part of the sphere.

Consider a circle of radius R centered at the origin ,

the required volume is ∫π(R2-x2)dx from -R to R/2 = 9πR3/8

Thus , ρObject=(9πR3/8)/(4πR3/3) * ρWater

=27/32 ρWater


I dunno if it's a legitimate method . It is suggested that I utilize the concept of hydrostatic pressure instead , but i have no idea how to do that.[/SUB]
 

Answers and Replies

  • #2
ehild
Homework Helper
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1,778
It is legitimate and correct. The buoyant force is equal to the weight of the displaced fluid.
 

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