An object of volume V and weight W is suspended below the surface of a stationary liquid o...

An object of volume V and weight W is suspended below the surface of a stationary liquid of weight density γ (Fig. a). Show that the tension in the cord is W – Vγ. In other words, show that the pressure distribution on the surface of the object exerts an upward force equal to the product of the object’s volume and the weight density of the water. This result is due to Archimedes (287–212 B.C.).

Strategy: Draw the free-body diagram of a volume of liquid that has the same shape and position as the object (Fig. b).