A piece of wood weighs 10 g in air. When a heavy piece of metal is suspended below it, the metal being submerged in water. The ' weight of wood in air + metal in water is 14 g . The 'weight ' when both the wood and metal are submerged in water is 2g . Find the volume and density of wood .

Let the volume of wood=Vw

volume of metal=Vm

density of wood=dw

density of metal=d_m

given,

Vwdw=10

Vmd_m-Vm=4

total weight of wood & metal-total bouyant force=apparant weight of both when emerged

(Vwdw+Vmdm)-Vmx(density of water)-Vwx(density of water)=2

(Vwdw-Vw)+(Vmdm-Vm)=2

putting the values from prev given equation:

(Vwdw-Vw)+4=2

Vw-Vwdw=2

Vw=2+10=12c

dw=10/12=0.833g/cc