Your friend is worried about a ring she bought on a recent trip to another count

Question

Your friend is worried about a ring she bought on a recent trip to another country. The ring was expensive and she was told it was pure gold, and she would like to know whether it is really 24 carat or not. You decide to help her with your extensive knowledge of physics and a good scale that reads to the nearest gram. Using a spring scale you weigh the ring and find that it has a weight of 0.153 N. Next you weigh the ring submerged in water and find a new reading of 0.142 N.

a) Is the ring pure gold?

b) Are you “certain”?

Explanation / Answer

in air, N = W = 0.153 N  

in water, N = W - Fb { Fb is buoyant force

Fb = rho_water V g }

0.142 = 0.153 - (1000 x V x 9.8)

V = 1.122 x 10^-6 m^2

and mass of ring = (0.153)/(9.8) = 0.0156 kg

density of ring = m /V = (0.0156) / (1.122 x 10^-6)

= 13914 kg/m^3

and density of gold is 19320 kg/m^3/

So this is not pure gold. Yes, Certain.

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