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ICSE Class 9 Answered

 A hollow metal cylinder of length  10 cm floats in alcohol of density 0.80 g per cm cube,  with 1 cm of its length above it.  What length of cylinder will be above copper sulphate solution of density 1.25 g per centimetre cube
Asked by rk2783740 | 31 Aug, 2018, 06:24: PM
answered-by-expert Expert Answer
when a floating object is partially immersed in liquid, mass of floating object is equal to the mass of displaced liquid.

Mass of displaced liquid is equal to the product of immersed volume of floating object(same as displaced volume of liquid) and liquid density.

when the cylider is partially immersed, immersed volume of cylinder is proportional to the height of cylider below water level.
 
hence we can write, when the hollow cylinder is immersed in alcohol, mass of cylinder = 9×C×0.8 ............(1)
where C is constant

Let us assume h is the immersed height (height below liquid surface) when the hollow cylinder is immersed in copper sulphate solution.
hence we can write, when the hollow cylinder is immersed in copper sulphate, mass of cylinder = h×C×1.25 ............(2)
 
if we equate (1) and (2), we get h as , h = (9×0.8)/1.25 = 5.76 cm
Answered by Thiyagarajan K | 03 Sep, 2018, 11:37: AM

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