Question

A triangular lamina of area \[A\] and height \[h\] is immersed in a liquid of density \[\rho \] in a vertical plane with its base on the surface of the liquid. The thrust on the lamina is
A. \[\dfrac{1}{2}A\rho gh\]
B. \[\dfrac{1}{3}A\rho gh\]
C. \[\dfrac{1}{6}A\rho gh\]
D. \[\dfrac{2}{3}A\rho gh\]

Answer 1

Hint:Thrust is the pressure exerted on the surface of the wooden block in a direction perpendicular to it, while pressure is a continuous force that is applied to the object against a body in contact with it. So, thrust is a force exerting on the object and the pressure is the force acting on the object per unit area.

Formulas used:
The formula to find the thrust acting on the lamina is given as,
\[\text{Thrust} = P \times A\]
Where \[P\] is the pressure and \[A\] is the area on which the thrust acts.
The formula used to find the pressure is given by,
\[P = h\rho g\]
Where \[h\] is the height, \[\rho \] is the density and \[g\] is the acceleration due to gravity.

Complete step by step answer:
The whole force of water will act at the centroid of the triangle. This point is at a distance of \[\dfrac{1}{3}h\] from the top surface of water. Now we find the pressure applied on the lamina using the formula,
\[P = h\rho g\]
When we substitute the height, we use \[\dfrac{1}{3}h\] and get,
\[P = \dfrac{{h\rho g}}{3}\]
Now that we have the value of pressure, we can find the thrust by using the formula, \[\text{Thrust} = P \times A\]
Substituting the values, we get
\[\text{Thrust} = P \times A \\
\Rightarrow \text{Thrust} =\dfrac{{h\rho g}}{3} \times A \\
\therefore \text{Thrust}= \dfrac{1}{3}A\rho gh\]

Therefore, the right answer is option B.

Note:Force acting on an object perpendicular to the surface is called thrust. It is a net force acting in a particular direction. It is always perpendicular to the surface on which force is applied. Thrust is a reaction force described quantitatively by Newton's Second and Third Laws. When a system expels or accelerates mass in one direction the accelerated mass will cause a proportional but opposite force on that system.