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?
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.
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.