Question

(a) Explain how increase of draught and of displacement influence rolling (6)

(b) A pontoon has a constant cross-section as shown in Fig. given below. The metacentric height is 2.5m. Find the height of the centre of gravity above the keel (10)

Answer 1

Part (a)

In case of increase of draught and displacement, this is a case of loading being done.

Thus, when the ship is being loaded, its GM will start to decrease.

Now, the time period of roll is given by:

$$T_{r}=\frac{2\pi k}{\sqrt{GM.g}}$$

Where,

k = radius of gyration
GM = metacentric height
g = acceleration due to gravity

Now, since, GM has started to decrease, the Tr will start to increase.

Thus, the ship will now roll with greater time period. Thus, an increase in draught and displacement, influences rolling.

✓ Verified Model Answer (Text Solution)

In case of increase of draught and displacement, this is a case of loading being done.

Now, the time period of roll is given by: