Question

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?

• A. Configuration P is stable and configuration Q is unstable.
• B. Both configurations are stable.
• C. Configuration P is unstable and configuration Q is stable.
• D. Both configurations are unstable.

Hint:

Compare the vertical order of G and M in each sketch; stability needs M above G.

Answer 1

The Correct Option is A

This question checks if you can read the relative position of G and M from a stability sketch and connect it to the sign of the metacentric height GM.

1. Configuration P is stable and configuration Q is unstable: In configuration P the point G sits below M, so GM is positive and any small heel creates a righting moment that pushes the ship back upright. In configuration Q, G sits above M, so GM is negative and a small heel grows into a capsizing moment. This matches the figure exactly, so it is correct.
2. Both configurations are stable: This would only hold if G stayed below M in both sketches, but in Q, G is clearly drawn above M, so this option is wrong.
3. Configuration P is unstable and configuration Q is stable: This reverses the actual positions shown in the figure and gives the opposite conclusion, so it is wrong.
4. Both configurations are unstable: This fails for P, where G sits below M and the ship is stable, so this option is wrong.

The correct choice is (A): configuration P is stable and configuration Q is unstable, because the metacentric height GM is positive in P and negative in Q.