Question

A beaker is sitting on a scale. Block A in the figure hangs by a cord from spring balance D and is submerged in a liquid C contained in beaker B. The mass of the beaker is 1.35kg; the mass of the liquid is 1.70kg. Balance D reads 3.55kg and balance E reads 7.50kg. The volume of block A is 3.90×10-3 m^3.

What is the density of the liquid?
p=? kg/m^3

What will the balance D read if block A is pulled up out of the liquid?

Mass D=? kg

What will the balance E read if block A is pulled up out of the liquid?

Mass E=? kg

Answer 1

When the block is in the liquid it exerts a downward force on the liquid equal to the buoyany force. So

Reading on scale E = mass of beaker + mass of liquid + mass of liquid displaced

7.50 = 1.35 + 1.70 + density * 0.0039

so... density of liquid = 1141 kg/m^3

Now... the current reading on scale D is the mass of the block minus the buoyant force. So...

reading on D = mass of block - mass of liquid displaced

3.55 = m - 1141*0.0039

m = 8.00 kg is the mass of the block

If the block is pulled out of the liquid, balance D will just read the mass of the block 8.00 kg

and balance E will just read the mass of the beaker and liquid = 3.05 kg