Buoyancy and Floatation

Question 1
A cylinder (2.0 m diameter, 3.0 m long and 25 kN weight) is acted upon by water on one side and oil (specific gravity=0.8) on other side as shown in the figure.

The absolute ratio of the net magnitude of vertical forces to the net magnitude of horizontal forces (round off to two decimal places) is _____________
A
0.61
B
1.22
C
0.22
D
0.94
GATE CE 2021 SET-1   Fluid Mechanics and Hydraulics
Question 1 Explanation: 


Net horizontal force \left(F_{H}\right) due to liquids
\begin{aligned} F_{H} &=F_{H 1}-F_{H 2} \\ &=\rho_{w} g \bar{h}_{1} A_{v_{1}}-\rho_{\mathrm{oil}} g \bar{h}_{2} A_{v_{2}} \\ &=\left(10^{3}\right)(9.81)\left(1+\frac{2}{2}\right)(2 \times 3)-(800)(9.81)\left(\frac{1}{2}\right)(1 \times 3) \\ F_{H} &=105.948 \mathrm{kN}(\rightarrow) \end{aligned}
Net vertical force \left(F_{v}\right) due to liquids
\begin{aligned} F_{v} &=F_{1}+F_{2} \\ &=\rho_{w} g \forall_{1}+\rho_{o i l} g \forall_{2} \\ &=\left(10^{3}\right)(9.81)\left(\frac{\pi(1)^{2} \times 3}{2}\right)+(800)(9.81)\left(\frac{\pi}{4}(1)^{2} \times 3\right) \\ &=64.7199 \mathrm{kN}(\uparrow) \\ \frac{F_{V}}{F_{H}} &=\frac{64.7199}{105.948}=0.61 \end{aligned}
Question 2
A body floating in a liquid is in a stable state of equilibrium if its
A
metacentre lies above its centre of gravity
B
metacentre lies below its centre of gravity
C
metacentre coincides with its centre of gravity
D
centre of gravity is below its centre of buoyancy
GATE CE 2020 SET-1   Fluid Mechanics and Hydraulics
Question 2 Explanation: 
For stability of floating body M lies above G
GM \gt 0
Question 3
For a body completely submerged in a fluid, the centre of gravity (G) and centre of Buoyancy (O) are known. The body is considered to be in stable equilibrium if
A
O does not coincide with the centre of mass of the displaced fluid
B
G coincides with the centre of mass of the displaced fluid
C
O lies below G
D
O lies above G
GATE CE 2011   Fluid Mechanics and Hydraulics
Question 3 Explanation: 
A completely submerged body will be in stable equilibrium when CG lies below the centre of buoyancy. It will be in unstable equilibrium when CG lies above the centre of buoyancy And when the CG coincides with the centre of buoyancy. The body will be in neutral equilibrium
Question 4
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
A
8.24
B
7.82
C
7.64
D
7.38
GATE CE 2001   Fluid Mechanics and Hydraulics
There are 4 questions to complete.

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