Let a be the side of the ice cube when it is about to be lifted.
At this instant the
mass of water formed = mass of ice melted.
Also the buoyant force = wt. Of remaining ice cube.
Let d1 be the density of ice and d2 be the density of water, so that
d1 / d2 = 0.9 -------------------------(1)
mass of water formed = volume of ice melted x density of ice
= [(4)3 - (a)3 ] d1 --------------------(2)
Volume of water formed = [(4)3 - (a)3 ] d1 / d2 ---------------(3)
Height to which water is formed = (Volume of water formed + Volume of ice immersed in the water.) / Area of the base of the cylinder.
H = {[(4)3 - (a)3 ] d1 / d2 + a2 H } / A --------------------------(4)
Where A = p r2 , r is the radius of the base of the cylinder
Buoyant force = a2 H d2 g --------------------- (5)
Wt. Of the remaining ice cube = a3 d1 g ------------------- (6)
From (4) , (5) and (6) we get the value of a .
Moderation Team
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