Question

A body weighs 70 gf in air and 45 gf in water. Determine the weight of the body in a liquid whose density is twice that of water.

• A. 10 gf
• B. 20 gf
• C. 30 gf
• D. 40 gf

Answer 1

The correct option is B

20 gf

Given :
$$\begin{gathered} \mathrm{weight}\mathrm{of}\mathrm{body}\mathrm{in}\mathrm{air}=70\mathrm{gf} \\ \mathrm{weightof}\mathrm{bdy}\mathrm{in}\mathrm{water}=45\mathrm{gf} \\ \mathrm{Density}\mathrm{of}\mathrm{liquid}=2{\mathrm{\rho }}_{\mathrm{w}}(\mathrm{where}{\mathrm{\rho }}_{\mathrm{w}}\mathrm{is}\mathrm{the}\mathrm{density}\mathrm{of}\mathrm{water}) \\ \mathrm{we}\mathrm{know}\mathrm{that}\mathrm{Relative}\mathrm{density}=\frac{\mathrm{Density}\mathrm{of}\mathrm{substance}}{\mathrm{Density}\mathrm{of}\mathrm{water}} \\ \Rightarrow \mathrm{Relative}\mathrm{density}\mathrm{of}\mathrm{liquid}=\frac{2\times \mathrm{density}\mathrm{of}\mathrm{water}}{\mathrm{density}\mathrm{of}\mathrm{water}} \\ \mathrm{relative}\mathrm{density}\mathrm{of}\mathrm{liquid}=2 \\ \mathrm{Apparent}\mathrm{loss}\mathrm{of}\mathrm{body}\mathrm{weight}\mathrm{in}\mathrm{given}\mathrm{water}={\mathrm{W}}_1-{\mathrm{W}}_2=70\mathrm{gf}-45\mathrm{gf}=25\mathrm{gf} \\ \mathrm{apparent}\mathrm{loss}\mathrm{of}\mathrm{body}\mathrm{weight}\mathrm{in}\mathrm{liquid}=70\mathrm{gf}-{\mathrm{W}}_3 \\ \mathrm{Inorder}\mathrm{to}\mathrm{find}\mathrm{the}\mathrm{weight}\mathrm{of}\mathrm{the}\mathrm{liquid}\mathrm{we}\mathrm{use}\mathrm{the}\mathrm{following}\mathrm{formula} \\ \mathrm{Relative}\mathrm{density}\mathrm{of}\mathrm{liquid}=\frac{{\mathrm{W}}_1-{\mathrm{W}}_3}{{\mathrm{W}}_1-{\mathrm{W}}_2} \\ \Rightarrow 2=\frac{70-{\mathrm{W}}_3}{25} \\ \Rightarrow {\mathrm{W}}_3=20\mathrm{gf} \\ \mathrm{Hence}\mathrm{option}\left(\mathrm{b}\right)\mathrm{is}\mathrm{the}\mathrm{correct}\mathrm{answer}. \end{gathered}$$