Question

A stationary object is fully submerged in a static fluid, as shown in the figure. Here, CG and CB stand for the center of gravity and the center of buoyancy, respectively. Which one(s) among the following statements is/are true?

• A. The object is in \textbf{stable} equilibrium if $y_{CG}>y_{CB}$.
• B. The object is in \textbf{stable} equilibrium if $y_{CG}
• C. The object is in \textbf{neutral} equilibrium if $y_{CG}=y_{CB}$.
• D. The object is in \textbf{unstable} equilibrium if $y_{CG}=y_{CB}$.

Hint:

For a {fully submerged} body in a homogeneous, static fluid: CB above CG $\Rightarrow$ stable; CB below CG $\Rightarrow$ unstable; CB coincident with CG $\Rightarrow$ neutral. (Here the $y$-axis points downward, so “above” means a {smaller} $y$.)

Answer 1

The Correct Option is A

Step 1: Forces on a fully submerged rigid body in a static fluid.
Two vertical forces act: weight $W$ (downward) through CG, and buoyancy $B$ (upward) through CB. When the body is slightly rotated, CG and CB remain fixed points relative to the body (the displaced volume equals the body volume), so the two forces form a couple whose sense determines stability.
Step 2: Stability criteria.
- If CB is above CG (i.e., CB at a smaller $y$ since $y$ increases downward), the upward buoyancy acting above the downward weight produces a {restoring} couple $\Rightarrow$ stable equilibrium. In coordinates: CB above CG $\iff y_{CB}<y_{CG} \iff y_{CG}>y_{CB}$. This matches statement (A) (true). - If CB is below CG ($y_{CB}>y_{CG}$), the couple is {overturning} $\Rightarrow$ unstable. Hence statement (B) is false. - If CB coincides with CG ($y_{CB}=y_{CG}$), the lines of action are collinear and no couple is produced for small rotations $\Rightarrow$ neutral equilibrium. Thus (C) is true and (D) is false. Final Answer: \[ \boxed{\text{(A) and (C)}} \]