A solid sphere of mass 8.6 kg, made of metal whose density is 3400 kg/m^3, hangs by a cord. When the sphere is immeresed in a liquid of unknown density, the tension in the cord is 38N. What is the density of the liquid?

1868.58 kg/m³

Explanation:

From Archimedes principle,

R. d = Density of object / density of liquid = Weight in air / Upthrust.

D/D' = W/U ... Equation 1

Where D = density of the solid sphere, D' = density of liquid, W = weight of solid sphere in air, U = upthrust of solid sphere in liquid.

Making D' the subject of the equation,

D' = D (U/W) ... Equation 2

Recall,

U = W-T ... Equation 3

Where m = mass of the solid sphere, g = acceleration due to gravity.

W = mg ... Equation 4

Where T = tension in the cord.

Given: m = 8.6 kg

constant: g = 9.81 m/s²,

Substitute into equation 4

W = 8.6 (9.81)

W = 84.366 N.

Also given: T = 38 N

Substitute into equation 3

U = 84.366-38

U = 46.366 N.

Finally, substituting into equation 2,

given that D = 3400 kg/m³

D' = 3400 (46.366/84.366)

D' = 1868.56 kg/m³

Hence the density of the liquid = 1868.58 kg/m³