An object hangs from a spring balance. The balance registers 32 N in air, 22 N when this object is immersed in water, and 27 N when the object is immersed in another liquid of unknown density. What is the density of that other liquid

500 kg/m³

Explanation:

From Archimedes principle,

R.d of the object = Weight of the object in air/upthrust of object in water = Density of the solid/Density of water

W/U = D/D' Equation 1

Where W = weight object in air, U = Upthrust of object in water, D = Density of object, D' = Density of water

Make D the subject of the equation

D = (W/U)D' Equation 2

Given: W = 32 N, U = 32-22 = 10 N, D' =  1000 kg/m³

Substitute into equation 2

D = (32/10)1000

D = 3200 kg/m³

Also,

R.d of the object = weight of the object in air/upthrust in liquid = Density of the object/ density of the liquid

W/U' = D/D''

Where U' = upthrust of the object in liquid, D'' = Density of the liquid

make D'' the subject of the equation

D'' = (U'/W)D Equation 3

Given: D = 3200 kg/m³, U' =  32-27 = 5 N, W = 32 N

substitute into equation 3

D''  = (5/32)3200

D'' = 500 kg/m³

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