Question

WEIGHT OF AN OBJECT IN AIR IS 80N AN WEIGHT OF THE SAME OBJECT IN WATER IS 60N. FIND THE RATIO BETWEEN THE DENSITY OF THE SUBSTANCE TO THE DENSITY OF WATER.

Answer 1

Dear Student,

$$\begin{gathered} \mathrm{Weight}\mathrm{of}\mathrm{object}\mathrm{in}\mathrm{air},{\mathrm{W}}_1=80\mathrm{N} \\ \mathrm{weight}\mathrm{of}\mathrm{object}\mathrm{in}\mathrm{water},{\mathrm{W}}_2=60\mathrm{N} \\ \mathrm{The}\mathrm{buoyant}\mathrm{force}\mathrm{is}=80-60=20\mathrm{N} \\ \mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2 \\ \mathrm{mass},\mathrm{m}=\frac{20}{10}=2\mathrm{kg} \\ \mathrm{means}2\mathrm{kg}\mathrm{water}\mathrm{is}\mathrm{displaced}\mathrm{by}\mathrm{the}\mathrm{object}. \\ \mathrm{Since}\mathrm{density}\mathrm{of}\mathrm{water},{\mathrm{d}}_2=1000\mathrm{kg}/{\mathrm{m}}^3,\mathrm{then}\mathrm{volume}\mathrm{of}\mathrm{water}\mathrm{is}, \\ \mathrm{V}=\frac{2}{1000}{\mathrm{m}}^3 \\ \mathrm{which}\mathrm{is}\mathrm{according}\mathrm{to}\mathrm{Archimedes}\mathrm{principle},\mathrm{is}\mathrm{the}\mathrm{volume}\mathrm{of}\mathrm{object}. \\ \mathrm{Density}\mathrm{of}\mathrm{object},{\mathrm{d}}_1=\frac{8}{{\displaystyle \frac{2}{1000}}}\mathrm{kg}/{\mathrm{m}}^3 \\ \frac{{\mathrm{d}}_1}{{\mathrm{d}}_2}=\frac{8\times 1000}{2}\times \frac{1}{1000}=4 \end{gathered}$$