Archimedes supposedly was asked to determine whether a crown made for the king consisted of puregold. According to legend, he solved this problem by weighing the crown first in air and then in water. Suppose the scale read 7.84 N with the crown in air and 6.84 N when it was in water. What should Archimedes have told the king

the crown was not made of pure gold

Explanation:

Mass of gold = weight in air / g = 7.84N/10ms-2 = 0.784 Kg or 0.8Kg

From Archimedes principle:

Upthrust = weight in air - weight in a fluid

Upthrust = volume * density * g

Note density of water = 1000kgm-3

7.84-6.84 = V * 1000kgm-3*10ms-2

V = 1/10000 = 1*10-4 m^3

Density = mass / volume = 0.8/1*10-4

= 8*10^3 Kgm-3

But we know the density of gold to be 19.3 * 10^3 kgm-3

Hence the crown was not made of pure gold