Chapter 14, Problem 1OQ

To determine

The dam which is built more strongly.

Answer to Problem 1OQ

Option (c) Both dams have equal strength.

Explanation of Solution

It is mentioned that both dams are of equal width. The first dam holds back a large lake and the second dam holds back a narrow river. Practically the size of water that a dam holds back is not the factor on which the strength of the dam is decided during construction. The strength of the dam is decided depending on the height above the ground it holds water.

The pressure of water at the bottom of the dam is given by the expression,

  $P=\rho gh$

Here, $P$ is the pressure, $\rho$ is the density of water, $g$ is the acceleration due to gravity, and $h$ is the height about which the water exist in the dam.

Assuming both reservoirs are equally high (that is water is equally deep), the pressure exerted by the water on the bottom of the dams will be same, the pressure is the same regardless the width of water the dams hold. Thus, Both dams have equal strength.

Conclusion:

Since both dams have equal strength, option (c) is correct.

The dam on the left has no extra strength as compared to the right and hence it does not possess more strength Thus, option (a) is incorrect.

The dam on the right has no extra strength as compared to the right and hence it does not possess more strength Thus, option (c) is incorrect.

The strength of the dams can be predicted from their height about which it holds water Thus, option (d) is incorrect.