Consider two configurations P and Q of a stationary ship floating in calm water with transverse sections as shown in the figure, where M is the metacentre, G is the centre of gravity, and B is the centre of buoyancy.
Which ONE of the following statements is TRUE regarding the static stability of the ship?
Show Hint
Compare the vertical order of G and M in each sketch; stability needs M above G.
Configuration P is stable and configuration Q is unstable.
Both configurations are stable.
Configuration P is unstable and configuration Q is stable.
Both configurations are unstable.
Show Solution
The Correct Option isA
Solution and Explanation
Step 1: Recall the stability condition.
A floating body is in stable equilibrium when its metacentre M lies above its centre of gravity G, so the metacentric height $GM = KM - KG$ is positive.
If G lies above M instead, GM turns negative and the body is unstable.
Step 2: Read the point order in configuration P.
In the sketch of configuration P, going up from the waterline, B is lowest, then G, then M sits highest.
So M is above G, which gives GM $> 0$, and configuration P is stable.
Step 3: Read the point order in configuration Q.
In configuration Q the order changes: B is lowest, then M, then G sits highest of all, above M.
So G is above M, which gives GM $< 0$, and configuration Q is unstable.
Final Answer:
Configuration P is stable and configuration Q is unstable.
\[ \text{P: GM > 0 (stable)}, \quad \text{Q: GM < 0 (unstable)} \]
