the weight of a body in water is one third of its weight in air. what is the density of the material of the body?

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Please find below the solution to the asked query:

$$\begin{gathered} \text{Suppose} \rho {\text{gm/cm}}^3 \text{is the density of the material. Density of water in} \\ {\text{water is 1 gm/cm}}^3\text{. So if W is the weight of the body in air, then weight} \\ \text{in water is }\frac{W}{3}\text{, the we have} \\ \frac{\text{density of body}}{\text{density of liquid}}=\frac{\text{weight of the body in air}}{\text{weight of the displaed liquid}} \\ \Rightarrow \frac{\rho }{1}=\frac{W}{W-{\displaystyle \frac{W}{3}}} \\ \Rightarrow \rho =\frac{3}{2} {\text{gm/cm}}^3 \end{gathered}$$

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