Question Bank • QB_PARAMETRIC_SWCE_STA_003MSQ • 2 Marks
Section 4: Soil and Water Conservation Engineering
Fluid Statics, Pressure & Manometry
Subtopic: Properties of fluid statics and buoyancy
Question Statement:
Which of the following statements regarding fluid statics and buoyancy is/are TRUE? (Variation QB_PARAMETRIC_SWCE_STA_003)
Options:
(A) The center of pressure on an inclined or vertical submerged surface always lies below its centroid
(B) For a floating body to be in stable equilibrium, its metacentric height ($GM$) must be positive ($GM > 0$)
(C) The buoyant force on a completely submerged body acts through the center of gravity of the displaced fluid
(D) In a static fluid, shear stress is non-zero along planes with maximum pressure gradients
Answer Key:
A, B, C
Step-by-Step Solution & Explanation
1. Center of pressure depth $h_{cp} = \bar{h} + \frac{I_{xx}}{\bar{h} A \sin^2 \theta} > \bar{h}$, so it lies strictly below the centroid for submerged non-horizontal surfaces (A is true).
2. A floating body is stable if the metacenter $M$ is above the center of gravity $G$, i.e., $GM > 0$ (B is true).
3. By Archimedes' principle, buoyancy acts through the centroid of displaced volume (center of buoyancy), which is the center of gravity of displaced fluid (C is true).
4. In a static fluid, shear stresses are identically zero everywhere regardless of pressure gradient; fluids cannot sustain static shear (D is false).