Question

A block of material of volume 20cm³ and density 24g/cm³ is suspended from a spring balance with half the volume the block immersed in water. What is the reading of the spring balance? (Density of water = 1.0g/cm³)

Answer 1

The weight of the block immersed in water

$$W=mg-g\rho_{\rm{w}} V_{\rm{im}}$$

So

$$W=g\rho_{\rm{b}}V_{\rm{b}}-g\rho_{\rm{w}}V_{\rm{b}}/2$$

$$=9.8\:\rm{N/kg}\times 24000\:\rm{kg/m^3}\times 20\times 10^{-6}\rm{m^3}$$

$$-9.8\:\rm{N/kg}\times 1000\:\rm{kg/m^3}\times 20\times 10^{-6}\rm{m^3}/2$$

$$=4.6\:\rm{N}$$