An ornament weighing `50g` in air weighs only `46 g` is water. Assuming that some copper is mixed with gold the prepare the ornament. Find the amount of copper in it. Specific gravity of gold is `20` and that of copper is 10.

Explanation

Let `m` be the mass of the copper in ornament. Then mass of gold in it is `(50 - m)`
Volume of copper `V_(1) = (m)/(10) (Volume = (mass)/(density))`
and volume of gold `V_(2) = (50 - m)/(20)`
When immersed in water `(rho_(w) = 1g//cm^(3))`
Decrease in weight = upthrust
`:. (50 - 46)g = (V_(1) - V_(2))rho_(w)g`
or `4 = (m)/(10) + (50 - m)/(20)`
or `80 = 2m + 50 - m`
`:. m = 30g`