Question

1. A cube (length of each side: 10 cm), made from some unknown material, floats on the surface of the ocean. If 72% of the total volume of this cube is underwater, determine: a) the total mass of water displaced by the cube b) the buoyant force acting on the cube c) the total mass of the object d) the density of the object

Answer 1

Length of the side a = 10 cm = 0.1 m

Volume of the cube V = a ³

                                = 10 ^-3 m ³

volume submerged V ' = 72 % of V = 0.72 V = 0.72x10 ^-3 m ³

(a).mass of the water displaced by the cube m = density of water x V '

      m = (1000 kg/m ³ )(0.72 x10 ^-3 )

         = 0.72 kg

(b).The buoyant force acting on the cube F = V ' g

        F = 0.72x10 ^-3 x 1000x9.8

           = 7.056 N

(c).Total mass of the object = mass of the water displaced.

                                        = 0.72 kg

(d). Density of the object D = mass / volume

                                        = 0.72 kg / 10 ^-3 m ³

                                        = 720 kg/m ³