Question

In a Dam, If we doubled the depth of the dam the hydrostatic force will be ?

Answer 1

Answer: Option (A) is the correct answer.

Explanation:

Force acting on a dam is as follows.

                  F = $\frac{1}{2}\rho g\omega H^{2}$ .......... (1)

Now, when we double the depth then it means H is increasing 2 times and then the above relation will be as follows.

                F' = $\frac{1}{2}\rho g\omega (2)^{2}$

               F' = $\frac{1}{2}\rho g\omega 4$ ........... (2)

Now, dividing equation (1) by equation (2) as follows.

          $\frac{F}{F'}$ = $\frac{\frac{1}{2}\rho g\omega H^{2}}{\frac{1}{2}\rho g\omega 4}$  

Cancelling the common terms we get the following.

                 $\frac{F}{F'}$ = $\frac{1}{4}$    

                   4F = F'

Thus, we can conclude that if doubled the depth of the dam the hydrostatic force will be 4F.