An ancient king’s supposedly golden crown had a mass of 3 kg, but it was actually made by a dishonest metal smith from an equal mix of gold (1.93 × 10⁴ kg/m³) and silver (1.06 × 10⁴ kg/m³).

(a) Suppose that Archimedes suspended the crown from a string and lowered it into water until it was fully submerged. If the string was then connected to a balance scale, what tension would Archimedes have measured in the string?

(b) If the test was repeated, but this time with the crown replaced by a 3-kg block of pure gold, what tension would be measured?