A cork of density 0.5 g cm3 floats on a calm swimming pool. The fraction of the corks volume which is under water is
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Given, density of cork = 0.5 g/cc
density of water = 1 g/cc (standard parameter)
Assume,
the total length of cork = l cm
the length of cork immersed = x cm
the cross sectional area of cork = A cm^2
For the cork to float, weight of the cork = buoyant force of water exerted on the cork
That implies,
l*A*(density of cork)*g = (density of liquid)*x*A*g [g = gravitational force]
On solving,
x/l = density of cork/density of liquid=0.5/1 = 0.5 g/cc
Volume of the fraction of cork (i.e., a cylinder) underwater = Area*height = A*(x/l) cm^3
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