(a) A rectangular, fully enclosed tank 2.4m long, 1.4m wide and 0.8m high is constructed of sheet metal weighing 443.6 kg-f (force). The tank floats in sea water of density 1025kg/m³ with its 0.8m sides vertical. If the centre of gravity is at the geometric centre of the vessel, calculate the metacentric height and comment on the stability of the tank.

International Edition---engineering Mechanics: Statics, 4th Edition
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Author:Andrew Pytel And Jaan Kiusalaas
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Chapter8: Centroids And Distributed Loads
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(a) A rectangular, fully enclosed tank 2.4m long, 1.4m wide and 0.8m high is
constructed of sheet metal weighing 443.6 kg-f (force). The tank floats in sea water
of density 1025kg/m³ with its 0.8m sides vertical. If the centre of gravity is at the
geometric centre of the vessel, calculate the metacentric height and comment on the
stability of the tank.
(b) A hydrometer is an instrument used for measuring the relative density of liquids
based on the concept of buoyancy. A particular hydrometer is 80 cm in length.
When placed in pure water, 50cm of the hydrometer is submerged and it reads
1.000 as shown in Figure 1.
i) Calculate the density of the hydrometer?
ii) When placed in Alcohol, 65 cm of the hydrometer is submerged beneath the
alcohol. Calculate the density of alcohol?
iii) Determine the reading of the hydrometer when it is in the alcohol?
iy What will happen when this hydrometer place in Pentane (p-625 kgm):
Fluid
surface
1.00
Hydrometer-
80 cm
50cm
Figure 1: A hydrometer
Transcribed Image Text:(a) A rectangular, fully enclosed tank 2.4m long, 1.4m wide and 0.8m high is constructed of sheet metal weighing 443.6 kg-f (force). The tank floats in sea water of density 1025kg/m³ with its 0.8m sides vertical. If the centre of gravity is at the geometric centre of the vessel, calculate the metacentric height and comment on the stability of the tank. (b) A hydrometer is an instrument used for measuring the relative density of liquids based on the concept of buoyancy. A particular hydrometer is 80 cm in length. When placed in pure water, 50cm of the hydrometer is submerged and it reads 1.000 as shown in Figure 1. i) Calculate the density of the hydrometer? ii) When placed in Alcohol, 65 cm of the hydrometer is submerged beneath the alcohol. Calculate the density of alcohol? iii) Determine the reading of the hydrometer when it is in the alcohol? iy What will happen when this hydrometer place in Pentane (p-625 kgm): Fluid surface 1.00 Hydrometer- 80 cm 50cm Figure 1: A hydrometer
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