Figure (a) below shows a solid cube hanging from a spring scale, with the scale measuring 5.40 N. In figure (b), the suspended cube is submerged in water, and the scale now reads 3.22 N. What is the density (in kg/m3) of the cube? (Hint: the free-body diagram to the right of figure (b) shows the forces acting on the cube, with B and T pointing up and Mg pointing down.) ScaleMga

Given: The weight of the cube is 5.40 N. The scale reading after the cube submerged in water is 3.22 N. Introduction: When a body is submerged in water then a buoyant force acts on the body in an upward direction, due to the buoyant force, the scale reading or the weight of the body is reduced. Calculation: Calculate the mass of the cube. m=Wg Here, m is the mass, W is the weight and g is the acceleration due to gravity. Substitute, 5.40 N for W and 9.80 m/s2 for g in the above expression. m=5.40 N9.80 m/s2m=0.5510 kg Calculate the buoyant force. FB=5.40 N-3.22 NFB=2.18 N Write the expression for the buoyant force. FB=ρgV Here, V is the volume, ρ is the density of the liquid. Substitute, 2.18 N for FB, 1000 kg/m3 for ρ and 9.80 m/s2 for g in the above expression. 2.18 N=1000 kg/m39.80 m/s2VV=2.18 N1000 kg/m39.80 m/s2V=0.00022245 m3 Write the density of the cube. ρcube=mV Substitute, 0.00022245 m3 for V and 0.5510 kg for m in the above expression. ρcube=0.5510 kg0.00022245 m3ρcube=2476.96 kg/m3 Thus, the density of the cube is 2476.96 kg/m3.