# Finding density of an object with the weight and density of fluid?

#### astupidummydumstupid

Hello, I am a bit stuck with a question

"A large container of water initially reads 0.485 kg. A ball is hung in the air from another set of scales which initially read 0.112 kg. The ball is lowered until it is fully submerged. The readings on both scales are now 0.496 kg and 0.101 kg respectively. What is the density of the ball?"

My working so far is here: https://imgur.com/a/sINtKX8

I have the volume of the fluid displaced and the density of the water which is provided, (p=1000kg m-3) but I'm unsure how to get the volume of the object in order to work out the density with the equation written in the far right (Vd/Vo=po/pf).

Would anyone know what the next step is?

Thank you (Thinking)

-I

#### Woody

Note that the change in reading of both scales is 0.011 kg
The volume of water displaced must equal the volume of the ball.

#### astupidummydumstupid

Hello, this must mean that

1 = pobj/1000

pobj = 1 x 1000

=1000

But this isn't the right answer. Is something wrong with my rearranging here maybe?

#### Woody

The Ball pushes a volume of water (equal to the balls own volume) out of the way,
however the displaced water "pushes back"
The Force pushing back is equal to the Weight of water displaced.

Be aware of the distinction between Weight (which is a force) and Mass (which isn't).

#### astupidummydumstupid

So the force pushing back is 0.11N, because 0.011 x 10 = 0.11 (using 10 as gravity instead of 9.8).

So 0.11/ (1000 x 10) = 1.1x10^-5 kgm-3

This is the volume, and since the volume of the object is equal, 1.1x10^-5 divided by itself is one, which leads me back to the same answer.

#### Woody

The change in Force measured by the scales is 0.11 Newtons (using g=10)

This implies a displacement of 0.011 kg of water,
This 0.011 kg of water is "trying to return to its original position"
(Ok this is anthropomorphizing a puddle of water, but sometimes it helps in the visualisation)
And pushing back against the ball with all its 0.11 Newtons of Weight.

1 kg of water has a volume of 1 litre (at standard room temperature and pressure).
Thus 0.011 kg of water has a volume of 0.011 litres
Thus the Ball has a volume of 0.011 litres.
The Ball has a mass of 0.112 kg.
Thus it is a very dense ball...

#### astupidummydumstupid

IT IS A DENSE BALL WHICH MEANS

p=m/V

And 0.112/1.1x10^-5 = 10181 = 10200kgm-3

IT'S VERY DENSE AND ALSO THE ANSWER THANK YOUUU! i cannot express my gratitude. Also, anthropromorphising not alive things is always useful, in every context, ever!

Thanks again!

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