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CBSE Class 11-science Answered

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.
Asked by gargpurvi85 | 13 Mar, 2015, 09:07: PM
answered-by-expert Expert Answer
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
 
begin mathsize 14px style Weight space of space the space space body space equals space Vρg Given space volume space of space body space immersed space in space liquid space of space density space straight rho subscript 1 space equals space straight V subscript 1 space end subscript and space volume space of space body space immersed space in space liquid space of space density space straight rho subscript 2 space equals space straight V subscript 2 space end subscript Therefore space we space can space write space according space to space the space law space of space floatation colon Buoyant space force space of space liquid space 1 space equals straight V subscript 1 space straight rho subscript 1 space straight g Buoyant space force space of space liquid space 2 space equals straight V subscript 2 space straight rho subscript 2 space straight g Weight space of space the space space body equals space Buoyant space force space of space liquid space 1 space plus space Buoyant space 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 rho subscript 2 plus straight V subscript 2 space straight rho subscript 2 space space space minus negative negative negative negative negative negative negative negative left parenthesis 3 right parenthesis Subtracting space left parenthesis 3 right parenthesis space from space left parenthesis 1 right parenthesis space we space get colon straight V space straight rho minus Vρ subscript 2 space equals 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 minus open parentheses straight V subscript 1 space straight rho subscript 2 plus straight V subscript 2 space straight rho subscript 2 close parentheses straight V left parenthesis space straight rho space minus straight rho subscript 2 right parenthesis space equals straight V subscript 1 space straight rho subscript 1 space minus straight V subscript 1 space straight rho subscript 2 straight i. 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
Answered by Jyothi Nair | 16 Mar, 2015, 11:52: AM

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