To determine the pressure at a certain point in a liquid with a free surface, you can use the hydrostatic pressure equation. This equation is given by:
[tex]\[ p = hdg \][/tex]
where:
- [tex]\( h \)[/tex] is the depth of the point below the surface (measured in meters, m),
- [tex]\( d \)[/tex] is the density of the liquid (measured in kilograms per cubic meter, kg/m³),
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately [tex]\( 9.81 \, \text{m/s}^2 \)[/tex]).
Let's briefly go over why this formula is correct:
1. Depth (h): The deeper you go into a liquid, the greater the pressure due to the weight of the liquid above.
2. Density (d): Heavier liquids (with higher density) exert more pressure at a given depth.
3. Gravity (g): Greater gravitational acceleration increases pressure for a given depth and density.
In hydrostatics, these quantities come together to determine the pressure exerted by the liquid at a particular depth. This relationship is encapsulated by the formula [tex]\( p = hdg \)[/tex].
Therefore, the correct choice from the given answer options is:
[tex]\[ \boxed{p = hdg} \][/tex]
