Question

A dam for water reservoir is built thicker at the bottom than at the top because:
A) Pressure of water is very large at the bottom due to its large depth.
B) Water is likely to have more density at the bottom due to its large depth
C) Quantity of water the bottom is very large
D) Variation in value of g

Answer 1

We will be evaluating the options, check for the factors due to which the thickness differs.
The dam is a structure that is used for retaining water and is built over water bodies (like rivers) and the reservoir is formed because of dams (for storing water only but not in very large quantities)

Complete step by step answer:
Pressure of a liquid in a container is given as;
$P = h\rho g$ _______________ (1)
Where,
P = Pressure
h = Height of container
$\rho$ = Density of the liquid
g = Gravitational constant
Evaluating the options:
A) Pressure of water is very large at the bottom due to its large depth: From (1), it can be seen that Pressure is directly proportional to height (depth) that means with the increase in height, the pressure also increases.
The pressure of water is greater at the bottom as compared to the top and hence thicker walls are required at the bottom to cope up with pressure.
B) Water is likely to have more density at the bottom due to its large depth: The density of any liquid is defined as mass per volume. The density of water will remain the same throughout. (997 $kg/{m^3}$ )
🡪This option gets canceled out.
C) Quantity of the bottom is very large: The quantity of water does not change. In terms of quantity, we would have required more area to increase capacity but not thicker walls, so this option gets cancelled out.
D) Variation in value of g: g is gravitational constant and its value is 9.8 $m/{s^2}$ which cannot be changed for different levels (top and bottom of reservoir) in the same place, so this option gets canceled as well.
Therefore, a dam for a water reservoir is built thicker at the bottom than at the top because the pressure of water is very large at the bottom due to its large depth, option A).

Note: In such questions, the relationships are found between different quantities through the formula so as to know the dependence and check the respective variations.
Constant is a term that is used for the quantities that have fixed values which do not change (can change under special conditions) e.g. g is gravitational constant and its value is 9.8 and this is applicable everywhere and it only becomes 0 at the center of the earth.