# A piece of wax weighs 18.80 g wt. in air. A piece of metal is found to weigh 17.03 g wt. in water. It is tied to the wax and both together weigh 15.23 g wt. in water. Find the relative density of wax?

Given,

Weight of wax in air, W1-air = 18.80 gwt = 18.80g dynes

Weight of metal in water, W2-water = 17.03 gwt = 17.03g dynes

Weight of wax and metal inside water, W1+2-water = 15.23 gwt = 15.23g dynes

Let the density of wax be d1 and volume of wax be V1, density of metal be d2 and volume be V2. Density of water be d.

Now,

W1-air = V1 d1 g = 18.80g

=> V1 d1 = 18.80 ………………(1)

W2-water = V2 d2 g – V2 d g

=> 17.03g = V2 d2 g – V2 d g

=> V2 d2 – V2 d = 17.03 ……………..(2)

W1+2-water = (V1 d1 g + V2 d2 g) – (V1 d g + V2 d g)

=> (V1 d1 g + V2 d2 g) – (V1 d g + V2 d g) = 15.23g

=> V1 d1 + V2 d2 – V1 d – V2 d = 15.23

=> 18.80 + (V2 d2 – V2 d) – V1 d = 15.23

=> 18.80 + 17.03 – V1 d = 15.23

=> V1 d = 18.80 + 17.03 – 15.23

=> V1 d = 20.6 ………………………(3)

(1)/(3) => d1/d = 18.8/20.6 = 0.913

This is the relative density of wax.

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