Question
Fri March 13, 2015 By: Shivangi Garg

When a body of mass 240kg is placed on an ice berg floating in sea water It’d  found that the ice berg just sinks. What is the mass of ice berg? Take relative density of ice 0 g and sea water 1.02 g/cm3?

Sir/Mam please let me know the detailed procedure of solving such problems also let me know the weight-age of marks such problems carry..

Expert Reply
Jyothi Nair
Sat March 14, 2015
The value of density of ice given is 0 but it is 0.9167 g/cm3
Therefore Density of ice berg =917 kg/cm3 and density of sea water = 1027 kg/cm3
 
begin mathsize 14px style According space to space the space law space of space floatation colon Mass space of space ice space berg plus space mass space of space the space body space equals space mass space of space the space displaced space sea space water space space minus negative negative left parenthesis 1 right parenthesis Let space straight M space be space the space mass space of space the space ice space berg space and space straight V space be space its space volume. Let space straight rho subscript ice space be space the space density space of space the space ice space berg Therefore colon Volume space of space the space ice space berg space equals fraction numerator Mass space of space the space ice space berg over denominator Density space of space ice space berg end fraction equals straight M over straight rho subscript ice space minus negative negative negative negative negative left parenthesis 2 right parenthesis Given space the space mass space of space the space body space equals space 240 space kg In space left parenthesis 1 right parenthesis Mass space of space the space displaced space water space equals Volume space of space the space ice space berg cross times Density space of space seawater space minus negative negative negative negative left parenthesis 3 right parenthesis Substituting space left parenthesis 2 right parenthesis space and space left parenthesis 3 right parenthesis space in space left parenthesis 1 right parenthesis space we space get colon straight M plus 240 space equals space Volume space of space the space ice space berg cross times Density space of space sea space water straight M plus 240 space equals straight M over straight rho subscript ice space cross times Density space of space sea space water straight M plus 240 space equals straight M over 917 cross times 1027 straight M plus 240 space equals 1.126 space straight M 200 equals left parenthesis 1.126 minus 1 right parenthesis straight M 200 equals 0.126 straight M straight M equals fraction numerator 240 over denominator 0.126 end fraction equals 1904.76 space kg    end style
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