It is given that the extended length in air is and the reduced length in water is .

We have to find the relative density of the weight. The ratio of longitudinal stress to longitudinal strain is called young's modulus of elasticity. Young modulus is given by the following formula.

Here, F is the force, l is the initial length of the wire, A is the area of cross-section, and is the change in the length of wire.

So, we can write the young's modulus for both air and water.

Now, we know that young's modulus is constant for the material, i.e., equation (1) is equal to equation (2).

Let us further simplify this.

We know, density is mass divided by volume.