Question

A piece of brass(alloy if copper snd zinc) weighs 12 9 gm in air. When completly immersed in liquid it weighs 11.3 gm. What is mass if copper contained in alloy. Relative densities of copper and zinc are 8.9 and 7.1 respectively

Answer 1

let the density of brass be  d.
let d_l = density of liquid
let d_c = density of copper
let d_z = density of zinc

Loss of weight in liquid  = 12.9 - 11.3 =  (12.9 /d) * d_l
           d / d_l = 12.9/1.6   ---- (1)

let there be m_c gm of copper and m_z gms of zinc in the alloy.

Total volume of brass piece = V = m_c / d_c  + m_z / d_z

Density d = (m_c + m_z) / V
   =>  d (m_c /d_c + m_z / d_z) =  m_c + m_z  ---- (2)

d_c = relative density of copper * density of liquid = 8.9 * d_l
d_z = relative density of zinc * density of liquid = 7.1 * d_l

Substituting in equation (2),
  (d/d_l) * (m_c /8.9  + m_z /7.1) =  m_c + m_z

now using equation 1, we get:
         m_c(1  - 0.9059) = m_z (1.1356 - 1)
             m_c =  1.441 m_z      ---- (3)

alloy weight = m_c + m_z = 12.9 gm    --- (4)

solving (3) and (4) we get   =>  m_z = 12.9/2.441 =  5.284 gms
     m_c =  7.616 gm