When a crown of mass 14.7kg is completely submerged in water, an accurate scale reading reads only 13.4kg. Is the crown made of gold?

No. The crown is made of lead

Explanation:

From Archimedes principle,

D/D' = W/U

Where D = density of the crown, D' = Density of water, W = weight of the crown in air, U = Upthrust of the crown in water.

make D the subject of the equation,

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

W = mg

Where g = 9.8 m/s², m = 14.7 kg.

W = 14.7 (9.8) = 144.06 N.

U = 9.8 (14.7-13.4) = 12.74 N.

Constant: D' = 1000 kg/m³

Substitute into equation 1

D = 1000 (144.06/12.74)

D = 11307.69 kg/m³

Density of the crown = 11307.69 kg/m³

And Density of Gold = 19300 kg/m³

From the above, The crown is not made of Gold