There is a cork weighing 30g. Determine what is the minimum mass of aluminum wire that must

There is a cork weighing 30g. Determine what is the minimum mass of aluminum wire that must be wrapped around the plug so that the plug and the wire are completely submerged in the water. Cork density 500 kg / m3, aluminum 2700 kg / m3, water 1000 kg / m3

According to the floating condition of bodies: ρ1 <ρ2.3, ρ1 is water (ρ1 = 1000 kg / m³), ρ2.3 is a plug with a wire. ρ2.3 = (m2 + m3) / V2.3, m2 = 30 g = 0.03 kg, V2.3 is the volume of the plug with wire (V2.3 = m2 / ρ2 + m3 / ρ3, ρ2 = 500 kg / m3, ρ3 = 2700 kg / m3). ρ2.3 = (m2 + m3) / V2.3 = (m2 + m3) / (m2 / ρ2 + m3 / ρ3). (m2 + m3) / (m2 / ρ2 + m3 / ρ3)> ρ1. m2 + m3> ρ1 (m2 / ρ2 + m3 / ρ3). 0.03 + m3> 1000 (0.03 / 500 + m3 / 2700). 0.03 + m3> 0.06 + 0.37m3. 0.63m3> 0.03. m3> 0.048 kg> 48 g.