Chapter 14: Q6Q (page 406)

Figure 14-24 shows three identical open-top containers filled to the brim with water; toy ducks float in two of them. Rank the containers and contents according to their weight, greatest first.

Short Answer

Expert verified

The rank of containers and contents according to their weight, greatest first is $W_{a} = W_{b} = W_{c}$

Step by step solution

The given data

Three containers are shown with different situations, where toy ducks float in two of them.

Understanding the concept of the buoyant force

For floating conditions, the buoyant force is balanced by the weight of the fluid displaced. The net force is due to the weight of the container only.

Formula:

The weight of the upward force applied on the body due to buoyancy,

$W_{b o d y} = ρ_{w a t e r} g V_{d i s p l a c e d}$ (i)

Calculation of the rank of the containers and contents according to their weight

For container (a), there is no object floating on water, so therewould be nochange in the weight.

For container (b) & (c), the duck is floating on water. Weight of the duck is balanced by the buoyant force. There is no change in the water level. So the total weight would remain the same considering equation (i), as no volume is displaced.

Hence, there would be no change in the weight of the container.

Therefore, the rank of containers and contents according to their weight is $W_{a} = W_{b} = W_{c} .$