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Class 4 (4th Engineer) SC&S 📅 May 2024

Exam Question

A hopper barge of box form 50 m long and 10 m wide floats at a draught of 2 m in seawater when the hopper, which is 15 m long and 5 m wide, is loaded with mud having relative density twice that of the seawater, to the level of the waterline. Doors in the bottom of the hopper are now opened allowing the mud to be discharged. Calculate the new draught. (16)

Reference Answer

### **Objective**
To calculate the final draught of a box-shaped hopper barge after discharging its cargo of mud by opening the bottom doors.
### **Principle**
This problem is solved by applying Archimedes' principle and the concept of 'lost buoyancy'. When the hopper doors are opened, two events occur simultaneously:

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