Question

A cork of density $0.15gc{m}^{-3}$ floats in water with $10c{m}^3$ of its volume above the surface of water. Calculate the mass of the cork.

Answer 1

Mass of cork = (10 + x ) * 0.15 g

volume of displaced water = x

mass of displaced water = x * 1 = x (density of water = 1 g cm-3)

As per the Archemedes' principle

weight of cork = weight of water displaced

x g= (1.5 + 0.15 x)g

x = 1.5 + 0.15 x

x = 1.5 / 0.85 = 1.765 cm3

total volume of the cork = 10+1.765 = 11.765 cm3

Mass of cork = 11.765 * 0.15 = 1.765 g