Question
Fri March 13, 2015 By: Shivangi Garg

A body of density p floats with a volume v1 of it's total volume  V immersed in one liquid of density p1and with the remaining volume V2 immersed in another liquid of density p2 where p1 > p2 find the relative volume immersed in liquids.

Expert Reply
Jyothi Nair
Mon March 16, 2015
Given the density of the body = ρ and volume = V
Therefore the mass of the body = Vρ
For a floating body in two liquids,
Weight of the body = Buoyant force of liquid 1 +Buoyant force of liquid 2
 
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force space of space liquid space 2 Vρg space equals space straight V subscript 1 space straight rho subscript 1 space straight g space plus space straight V subscript 2 space straight rho subscript 2 space straight g Vρ space equals space straight V subscript 1 space straight rho subscript 1 space space plus space straight V subscript 2 space straight rho subscript 2 space end subscript space space space minus negative negative negative negative negative negative negative space left parenthesis 1 right parenthesis Also comma space straight V space equals straight V subscript 1 space plus straight V subscript 2 space space space space space space minus negative negative negative negative negative negative negative negative left parenthesis 2 right parenthesis On space multiplying space left parenthesis 2 right parenthesis space space with space straight rho subscript 1 space we space get colon straight V space straight rho subscript 2 space equals straight V subscript 1 space straight 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straight e. space straight V left parenthesis space straight rho space minus straight rho subscript 2 right parenthesis space space equals straight V subscript 1 space left parenthesis straight rho subscript 1 space minus straight rho subscript 2 space right parenthesis rightwards double arrow space straight V subscript 1 space equals open parentheses fraction numerator straight rho space minus straight rho subscript 2 over denominator straight rho subscript 1 space minus straight rho subscript 2 end fraction close parentheses straight V Similarly space on space multiplying space left parenthesis 2 right parenthesis space by space straight rho subscript 1 space we space get colon Vρ subscript 1 space equals straight V subscript 1 space straight rho subscript 1 space plus straight V subscript 2 space straight rho subscript 1 space space space minus negative negative negative negative negative negative negative negative negative left parenthesis 4 right parenthesis  Subtracting space left parenthesis 4 right parenthesis space from space left parenthesis 1 right parenthesis space we space get colon Vρ subscript 1 space space minus Vρ space equals open parentheses straight V subscript 1 space straight rho subscript 1 space plus straight V subscript 2 space straight rho subscript 1 close parentheses space minus space open parentheses straight V subscript 1 space straight rho subscript 1 space space plus space straight V subscript 2 space straight rho subscript 2 space end subscript close parentheses straight V left parenthesis space straight rho subscript 1 space minus straight rho space right parenthesis space equals straight V subscript 2 open parentheses straight rho subscript 1 space minus straight rho subscript 2 close parentheses rightwards double arrow straight V subscript 2 space equals open parentheses fraction numerator space straight rho subscript 1 space minus straight rho over denominator straight rho subscript 1 space minus straight rho subscript 2 end fraction close parentheses straight V    end style
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