Two solids  P and Q float in water. It is observed that P floats with half its volume immersed and Q floats with 2/3rds of its volume immersed.  What are the ratio of densities of Pand Q? 

Asked by Malavika Umesh | 4th May, 2015, 09:23: PM

Expert Answer:

According to the principle of floatation, when a body floats, the weight of the body must be equal weight of the displaced volume of liquid.
Let V1 and dbe the volume and density of body P and V2  and d2 be the volume and density of body Q.

For body P to float:
begin mathsize 14px style straight V subscript 1 cross times straight d subscript 1 cross times straight g equals straight V subscript 1 over 2 cross times 1 cross times straight g straight d subscript 1 equals 1 half for space body space straight Q space to space float colon straight V subscript 2 cross times straight d subscript 2 cross times straight g equals 2 over 3 straight V subscript 2 cross times 1 cross times straight g straight d subscript 2 space equals 2 over 3 Therefore colon fraction numerator straight d subscript 1 over denominator straight d subscript 2 space end fraction equals fraction numerator 1 half over denominator 2 over 3 end fraction fraction numerator straight d subscript 1 over denominator straight d subscript 2 space end fraction equals 3 colon 4 end style

Answered by Jyothi Nair | 5th May, 2015, 10:18: AM

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