Question:hard
A ship consumes 250 tonne of fuel when moving from sea to a river. On arrival, draught and trim (measured at rest) are the same as the corresponding values at sea.
The displacement of the ship in seawater is ______ tonne (answer in integer).
The density of seawater and river water are 1025 kg/m\(^3\) and 1000 kg/m\(^3\) respectively.
A ship consumes 250 tonne of fuel when moving from sea to a river. On arrival, draught and trim (measured at rest) are the same as the corresponding values at sea.
The displacement of the ship in seawater is ______ tonne (answer in integer).
The density of seawater and river water are 1025 kg/m\(^3\) and 1000 kg/m\(^3\) respectively.
The displacement of the ship in seawater is ______ tonne (answer in integer).
The density of seawater and river water are 1025 kg/m\(^3\) and 1000 kg/m\(^3\) respectively.
Show Hint
Same draught in both waters means the underwater volume is unchanged, only the density differs.
Updated On: Jul 28, 2026
Show Solution
Correct Answer: 10250
Solution and Explanation
Step 1: Fix the unknown as the shared underwater volume.
Call the submerged volume $V$. Because the draught and trim at the river are identical to those at sea, this same $V$ applies in both places.
Step 2: Express both displacements through V and take the difference.
Displacement equals density times volume, so at sea $W_{sea} = 1.025V$ tonne (density in tonne/m$^3$) and in the river $W_{river} = 1.000V$ tonne. Fuel burned reduces the ship's weight, and this loss must equal the reduction predicted purely from the volume being fixed: $W_{sea} - W_{river} = (1.025 - 1.000)V = 0.025V$.
Step 3: Use the fuel burned to find V, then the seawater displacement.
Setting $0.025V = 250$ tonne gives $V = 10000$ m$^3$. The displacement in seawater is then $W_{sea} = 1.025 \times 10000 = 10250$ tonne.
Final Answer:
The ship displaces 10250 tonne of seawater. \[ \boxed{W_{sea} = 10250 \text{ tonne}} \]
Call the submerged volume $V$. Because the draught and trim at the river are identical to those at sea, this same $V$ applies in both places.
Step 2: Express both displacements through V and take the difference.
Displacement equals density times volume, so at sea $W_{sea} = 1.025V$ tonne (density in tonne/m$^3$) and in the river $W_{river} = 1.000V$ tonne. Fuel burned reduces the ship's weight, and this loss must equal the reduction predicted purely from the volume being fixed: $W_{sea} - W_{river} = (1.025 - 1.000)V = 0.025V$.
Step 3: Use the fuel burned to find V, then the seawater displacement.
Setting $0.025V = 250$ tonne gives $V = 10000$ m$^3$. The displacement in seawater is then $W_{sea} = 1.025 \times 10000 = 10250$ tonne.
Final Answer:
The ship displaces 10250 tonne of seawater. \[ \boxed{W_{sea} = 10250 \text{ tonne}} \]
Was this answer helpful?
0
