Suppose the glass of the previous problem is covered by a jar and the air inside the jar is completely pumped out. (a) What will be the answers to the problem? (b) Show that the answers do not change if a glass of different shape is used provided the height, the bottom area and the volume are unchanged.

Question

Philoid · Accepted Answer

(a) Here, we are removing the atmospheric pressure.

Hence, pressure at the bottom of the glass,

Therefore, the downward force is given by .

For the second case, the vertical force is equal to the weight of the water,

The horizontal forces again cancel out. So the total upward force is,

The total force on the bottom depends only on the height of the vessel, the bottom area and the weight of the water. As density of water is fixed, the total force thus depends on the volume of the container. These quantities can remain same for different shapes and hence the answers do not depend on the shape of the container.