Centre of Buoyancy

Q. As depth of immersion of a vertical plane surface increases, the location of centre of pressure

1. comes closer to the centre of gravity of the area
2. moves apart from the centre of gravity of the area
3. ultimately coincides with the centre of gravity of the area
4. remains unaffected

Q. The stable equilibrium is achieved in the floating body when ?

1. Center of gravity is below the center of buoyancy.
2. Metacenter is above the center of gravity.
3. Metacenter is below the center of gravity.
4. Metacentric height is zero.

Q. A 15 cm length of steel rod with relative density of 7.4 is submerged in a two layer fluid. The bottom layer is mercury and the top layer is water. The height of top surface of the rod above the liquid interface in 'cm' is

1. 8.24
2. 7.82
3. 7.64
4. 7.38

Q. A symmetrical right-circular cone of wood floats in fresh water with axis vertical and the apex down. The axial height of the cone is 1 unit. The submerged portion has a height h, measured upwards from the apex. What would be the height of the centre of buoyancy from the apex?

1. $\frac{h}{2}$
2. $\frac{5}{8}h$
3. $\frac{2}{3}h$
4. $\frac{3}{4}h$

Q. For a floating body, buoyant force acts at the

1. centroid of the floating body
2. center of gravity of the body
3. centroid of the fluid vertically below the body
4. centroid of the displaced fluid

Q. In an iceberg, 15% of the volume projects above the sea surface. If the specific weight of sea water is 10.5 kN/m${}^3$, the specific weight of iceberg in kN/m${}^3$ is

1. $12.52$
2. $9.81$
3. $8.93$
4. $7.83$

Q. Consider the following statements related to buoyancy in fluid statics:
1. Principle of buoyancy is applicable both to floating bodies and to submerged bodies.
2. Archimedes formulated the first theory of buoyancy.
3. In analyzing buoyancy of a floating body it is assumed that the resultant vertical force passes through centre of pressure.
4. In a free-body diagram of a floating body summation of all horizontal forces is taken as zero.
Which of these statements are correct?

1. 1, 3 and 4
2. 1, 2 and 4
3. 1, 2 and 3
4. 2, 3 and 4

Q. A circular disc of diameter d is immersed vertically in a liquid of density P. The top most point of the disc just touches the liquid surface. What is the depth of Centre of pressure ?

1. $\frac{3}{8}D$
2. $\frac{5}{4}D$
3. $\frac{5}{8}D$
4. $\frac{3}{4}D$

Q. A cube of side 100 mm is placed at the bottom of an empty container on one of its faces. The density of the material of the cube is 800 kg/$m^3$ . Liquid of density 1000kg/$m^3$ is now poured into the container. The minimum height to which the liquid needs to be poured into the container for the cube to just lift up is______mm.

1. 80

Q. The large vessel shown in the figure contains oil and water. A body is submerged at the interface of oil and water such that 45 percent of its volume is in oil while the rest is in water. The density of the body is_____kg/$m^3$.
The specific gravity of oil is 0.7 and density of water is 1000 kg/$m^3$.
Acceleration due to gravity: g=10 m/$s^2$.

1. 865

Q. An aluminium alloy (density 2600 kg/$m^3$) casting is to be produced. A cylindrical hole of 100 mm diameter and 100 mm length is made in the casting using sand core (density 1600 kg/$m^3$) . The net buoyancy force (in Newton) acting on the core is_____

1. 7.7

Q. Consider the figure below relating to buoyancy in water.
What will be the downward force upon the top of the body ABCDEF?

1. The weight of the liquid column ABCHG
2. The weight of the liquid column DEFGH
3. The weight of the liquid column ABCHG -the weight of the liquid column DEFGH
4. The weight of the liquid column ABCHG + the weight of the liquid column DEFGH

Q. A cylindrical body of cross-sectional area A, height H and density ${\rho }_{s^{\prime }}$ is immersed to a depth h in a liquid of density $\rho$, and tied to the bottom with a string. The tension in the string is

1. $\rho ghA$
2. $({\rho }_s-\rho )ghA$
3. $(\rho -{\rho }_s)ghA$
4. $(\rho h-{\rho }_{s}H)gA$