Question

Consider the following statements: The increase in metacentric height

1) Increases stability

2) Decreases stability

3) Increases comfort for passengers in a ship

4) Decreases comfort for passengers is a ship

Which of the above statements are correct?
1. 1 and 3
2. 1 and 4
3. 2 and 3
4. 2 and 4

Answer 1

Correct Answer - Option 2 : 1 and 4

Concept:

Metacentric height of ship and period of oscillation of ship is related as,

\(T = 2\pi \sqrt {\frac{{{K^2}}}{{gh}}}\)

Where,

K = radius of gyration of the body about a longitudinal axis passing through the center of gravity.

h = metacentric height

g = acceleration due to gravity

Conclusion:

• An increase in metacentric height increases the stability of the ship but at the same time, it reduces the period of oscillation.
• A low period of oscillation causes sharp vibrations to ship which are quite uncomfortable to passengers on board.