Question

As we move downwards inside a stationary liquid of density'd'through a depth 'z', how does the pressure varies?

• A. Pressure increases by a factor 'dgz'.
• B. Pressure reduces by a factor 'dgz'
• C. There will be no change in pressure
• D. May increase or decrease depending upon density

Answer 1

The correct option is A

Pressure increases by a factor 'dgz'.

Consider two cases

Case 1 A plate at a depth$h_1$ in water and

case 2 A plate at a depth $h_2$ in water $h_1<h_2$
We can obviously see that the Force on the plates in case (ii) will be greater. As the number of balls on and top of it is greater. Let us assume that the area of the plate is 'A' and the density of the liquid is $\rho$
.

As the thickness is negligible force from the top and the bottom will be the same.

$F_1=m_{1}g{F}_2=m_{2}g$
$=\rho V_{1}g=\rho V_{2}g$
$=\rho A{h}_{1}g=\rho A{h}_{2}g$
$P_1=\frac{F_1}{A}=\rho g{h}_1{P}_2=\frac{F_2}{A}=\rho g{h}_2$
$\therefore$ Therefore as depth increases pressure increases.