Question

(i)A piece of brass (cu and zn)weighs 12.9 g in air.When completely immersed in water it weighs 11.3g.The relative densities of cu and Zn are 8.9 and 7.1 respectively.The mass of copper in the alloy is what
(ii)A piece of an alloy of mass 96 gm is composed of 2 metals whose specific gravities are 11.4 and 7.4.If the weight of alloy is 86 gm in water then the mass of each metal in the alloy will be
(iii)A balloon contains 400m^3 of hydrogen.If mass of the balloon without hydrogen is 34 g.Its net lifting ability is (density of hydrogen is 6.9 kg/m^3 density of air= 1.3 kg/m^3)
Please explain the questions with proper explanations and answer all the questions and step by step explanation

Answer 1

Density of brass = d gm/cm³.  let its volume be V cm³.
acceleration due to gravity = g

Weight in air = V d  = 12.9 gms

Apparent Weight in water = V d - V * 1  = V (d -1) = 11.3  gms 
          Hence V = 1.6 cm³
           d = 12.9 / 1.6 = 8.0625 gms/cm³

Proportions of copper and zinc  :    c : (1-c)    in the alloy of brass

              hence, c * 8.9 + (1-c) * 7.1 = 8.0625 
                       c = 0.535  =>  Copper is 53.5 % in the alloy.

mass of copper element in the alloy = 53.5/100 * 12.9 gms = 6.9015 gms
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Relative Density of alloy = 96 / (96 - 86) = 9.6    =   wt in air / (wt in air - wt in water)
   Weight of substance 1 = w1 gm in the alloy

                 (w1/96) * 11.4 + (1 - w1/96) 7.4 = 9.6
                 4 w1 = 2.2 * 96
                       w1 = 52.8 gms

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are u sure of the weight of balloon with out hydrogen is 34 gms ?? is it 34 kg ??
are u sure of the densities given ??    hydrogen density is 89 gms/m³ 

weight of hydrogen in the balloon = (89/1000) *400 = 35.6 kg 
Total weight of balloon with hydrogen = 35.634 kg   or   35.634*g  newtons

The buoyancy force on it = 400 m³ * 1.3 kg/m³ * g = 520*g  newtons 
taking the acceleration due to gravity as g.

Net force lifting the balloon upwards = 520 g - 35.634 g  newtons 
                       = 484.366 g  Newtons 

Net lifting ability or the load it can carry = 484.366 kg