Question

a cork of density 0.15 gm/cm^3 floats in water with 10 cm^3 of its volume above surface of water. calculate mass of cork

Answer 1

let 'x' cm3 of the cork is under water 

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