A cube of wood floating in water supports a 300 g mass at the centre of its top face. When the mass is removed, the cube rises by 3 cm. Determine the volume of the cube.

Explanation

Let each side of the cube be l. The volume occuied by 3 cm depth of cube,
`V = (3 cm) xx l^2 = 3 l^2 cm^3`
According to the principle of floatation, we have,
`V rho g = mg implies V rho = m`
`rho` is density of water = `1000 kg m^(-3)`
`implies (3 l^2 xx 10^(-2)m) xx (1000 kg m^(-3)) = 300 xx 10^(-3) kg`
`l^2 = (300 xx 10^(-3))/(3 xx 10^(-2) xx 1000) m^2 implies l^2 = 100 xx 10^(-4) m^2`
`l = 10 xx 10^(-2) m = 10 cm`
Therefore, volumne of cube = `V = l^3 = 1000 cm^3`