Question

A ship floating in seawater has a TPC (Tonne Per Centimeter immersion) of 20.

If bilge keel of total mass 65.1 tonne and volume 44 \(\text{m}^3\) is added to the ship, then the change in the mean draft is ______ cm.

Assume that after bilge keel fitment, the TPC remains constant, and the ship undergoes parallel sinkage. Density of seawater is 1025 \(\text{kg/m}^3\).

• A. 0.5
• B. 1
• C. 0.55
• D. 1.1

Hint:

Subtract the buoyancy from the keel's own volume before dividing the rest by TPC.

Answer 1

The Correct Option is B

This question checks whether you remember that TPC alone is not enough when the added object also has its own submerged volume, since part of its weight is carried by that displacement.

1. 0.5 cm: This comes from ignoring the keel's volume and using only a fraction of its weight, so it does not match either the given mass or volume.
2. 1 cm: The keel's volume of 44 cubic metres displaces 44 times 1.025, which is 45.1 tonne of seawater on its own. That leaves 65.1 minus 45.1, or 20 tonne, to be carried by parallel sinkage. Dividing 20 tonne by the TPC of 20 gives exactly 1 cm, so this is correct.
3. 0.55 cm: This would follow from taking half the correct sinkage or misreading the TPC value, and it does not follow from the given numbers.
4. 1.1 cm: This overshoots because it treats the full 65.1 tonne as needing parallel sinkage without subtracting the buoyancy the keel volume already gives.

The correct choice is (B): the mean draft changes by 1 cm once the keel's own displaced volume is accounted for.