Question

A thin rectangular plate of area A is immersed in water vertically . The length of the vertical side immersed in water is h .The thrust on one side of the plate due to water ( density of water = p ) is ( neglect atmospheric pressure )

Answer 1

Answer: The thrust on one side of the plate is $F = \rho g A\dfrac{h}{2}$

Explanation:

Given that,

Length = h

Density of water =$\rho$

Area = A = xh

Here, we considered x is a width and it is constant.

h is the total height of thin rectangular plate.

We know that,

The thrust is

$F = P\times A$

Let us considered an element at y height of dy thickness.

$dF = dP(A)$

$dF = \rho g y\times xdy$

$dF = \rho g x (y dy)$

On integrating

$F= \int_{0}^{h}\rho g x(y dy)$

$F= \rho g x \dfrac{h^{2}}{2}$

$F= \rho g A\dfrac{h}{2}$

Where, xh = A

Hence, the thrust on one side of the plate is $F = \rho g A\dfrac{h}{2}$