Question

The given figure shows the cross-section of a dam and its reservoir. The widening of the wall, towards the bottom, is because of __________.

A. increase in pressure with the depth of water
B. decrease in pressure with the depth of water
C. change in density of water
D. increase in the mass of the wall

Answer 1

Hint: Since the thickness of the wall is seen to increase with an increase in depth, we could think of the property of water that changes with depth. Cross-check which among the given options best describes the reason for the increase in the thickness of the wall. Also, remember density remains the same for an increase in depth.
Formula used:
The pressure at depth h,
$P\left( h \right)={{P}_{0}}+\rho gh$

Complete step by step solution:
In the question, we are given the cross-section of a dam and its reservoir and we are asked to find the reason for the widening of the wall with an increase in depth.
Let us recall expression for pressure at a point which is at a depth of h from the surface of the water which is given by,
$P\left( h \right)={{P}_{0}}+\rho gh$
Where, ${{P}_{0}}$ is the atmospheric pressure at the surface of the water, $\rho $ is the density of the water, g is the acceleration due to gravity and h is the depth of the point at which the pressure is to be found.
So from the above relation, we see that as the depth increases, the pressure also increases along with it.
So in order for the wall to withstand this greater pressure with an increase in depth, the wall has to be built wider. Thus building the wall of the dam wider increases the stability of the dam.
Therefore, we found that the widening of the wall, towards the bottom, is because of an increase in pressure with the depth of water. Hence, option A is the right answer.

Note: Some of the other places where the effect of the increase in pressure with depth is withstood are:
(a) Reinforced diving suit worn by deep-sea divers.
(b) Glasses used in the windows of underwater survey vessels are always very thick.
(c) Water supply tanks are kept very high for the fast flow of water through tapes.