A wooden sphere of radius `1.0 cm` sinks in water. On coating it with a layer of wax of uniform thickness `3 mm`, it just floats. What is the density of wood ? Density of wax `= 0.8 g//cm^3`.

Explanation

Volume of wooden ball `= (4 pi)/(3) (1)^3 = (4 pi)/(3)`
Volume of ball coated with wax `= (4 pi)/(3) (1.3)^3`
Volume of wax `=(4 pi)/(3)[(1.3)^3 - 1]`
Upthurst, `F_B = (4 pi)/(3) (1.3)^3 xx 1 xx g` (as `rho_w` = density water `= 1 g//cm^3`)
For the ball coated with wax to just float on water,
`F_B = ((4 pi)/(3)) rho g + ((4 pi)/(3)) [(1.3)^3 - 1] (0.8)g`
or `(4 pi)/(3) (1.3)^3 g = ((4 pi)/(3)) rho g + ((4 pi)/(3)) [(1.3)^3 - 1](0.8) g`
whence, `rho = (1.3)^3 - (1.3)^3(0.8) + 0.8`
=`(1.3)^3 (0.2) + 0.8`
=`1.24 g//cm^3`.