How can the work required to remove a solid ball from water be calculated?

[Copycat91]

Homework Statement

A solid ball with radius r and mass m is located inside an opened wide tank filled with water. The ball has the same density with water.
http://3.bp.blogspot.com/_jn57XA2jL...41pJXdRc/s1600-h/Get+Ball+Out+from+Water.jpg"
Calculate work required to get the ball out from the water!
Ignore viscosity and surface tension.

Homework Equations

F_buoy = ρgV
F_grav = -mg

The Attempt at a Solution

I have found its answer, W = mgr, but http://collectionofphysicsproblems.blogspot.com/" , it says there's a tricky solution.
I hope anyone could help on finding the tricky solution.
Thanks.
http://collectionofphysicsproblems.blogspot.com/"

 

[chrisk]

Use Archimedes' Principle to figure this one. Think about the amount of water displaced when the ball is completely submerged.

 

[Copycat91]

Hmm...
Wouldn't it really need integral?
If I use archimedes buoyancy force, it would...
W=integral(ρgV dh)

 

[chrisk]

An integration is not required. Archimedes Principle states the bouyant force is equal to the amount of fluid displaced. The ball has the same density of water so it neutrally bouyant (bouyant force equals gravitational force). So, an infinitesimal amount of force will move the ball (ignoring viscosity) in any direction. But work was done on the water when the ball was completely submerged (water level increased). Conservation of energy states the same amount of work is required to remove the ball from the tank.

 

[vivekrai]

It is given that the tank is wide, so the rise in the level of liquid is ~~ negligible.
and Neither we have dimensions for tank.