Question

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

A) 4F

B) F/2

C) 2F

D) F/4

Answer 1

Answer: Option (A) is the correct answer.

Step-by-step explanation:

Force acting on a dam is as follows.

F =
`(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' =
`(1)/(2)\rho g\omega (2)^(2)`

F' =
`(1)/(2)\rho g\omega 4` ........... (2)

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

`(F)/(F')` =
`((1)/(2)\rho g\omega H^(2))/((1)/(2)\rho g\omega 4)`

Cancelling the common terms we get the following.

`(F)/(F')` =
`(1)/(4)`

4F = F'

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