A plane surface of area A in the - y plane is subjected to a uniform pressure p 0 . Show that this distributed load can be represented by an equivalent force of magnitude p 0 A whose line of action...

A plane surface of area
A
in the
-y
plane is subjected to a uniform pressure
p
₀. Show that this distributed load can be represented by an equivalent force of magnitude
p
₀
A
whose line of action passes through the centroid of
A.

Strategy: Write integral expressions for the total force and the total moment about the origin due to the uniform pressure, and use the definitions of the centroid of an area.