Question

A metal cube of side 2cm and weight of 24g in air . Find the apparent weight when submerged in a) water b) alcohol of density of 0.8 g/cm3

Answer 1

The apparent weight of the cube when it submerged is liquid is given by

$$m'=\frac{W}{g}=\frac{mg-g\rho V}{g}=m-\rho V.$$

(a) in water $\rho_W=1\:\rm g/cm^3,$ so

$$m'=24\:\rm g-1\:\rm g/cm^3\times (2\:\rm cm)^3=16\:\rm g.$$

(b) in alcohol $\rho_A=0.8\:\rm g/cm^3,$ so

$$m'=24\:\rm g-0.8\:\rm g/cm^3\times (2\:\rm cm)^3=17.6\:\rm g.$$