Chapter 10, Problem 3Q

To determine

To explain: The hydrostatic paradox of the given situation.

Explanation of Solution

Introduction:

At equilibrium, at a certain point within the liquid, the pressure that is exerted by the fluid due to the force of gravity can be defined as the hydrostatic pressure.

The weight of the water can be given by the following expression: $W=mg$ for each container giving different mass.

In case of first container, the weight can be given as: $W_1=m_{1}g$

Similarly, to balance this downward force, there is upward force acting on the water which will be equal to the weight: $F_1=m_{1}g$

In case of second container, the mass of the water is different. So, due to greater mass the weight of the second container will be higher than the upward force. To balance the net force, there will be an extra amount of upward force that depends on the slanted shaped walls of the container pushing the water. Hence, the force will be balanced.

In third container, the weight of the water will be lesser than the upward force.

Due to the hydrostatic pressure, the force on each container is always perpendicular to the water’s surface. Hence, according to Newton’s third law of motion, the force acting on the container is perpendicular and opposite to the surface of the water.

Conclusion:

Hence, the total weight of the water is different for each container.