Q1GATE 2021NAT

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 _____________

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📖 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}

Q2GATE 2020MCQ

A body floating in a liquid is in a stable state of equilibrium if its

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📖 Explanation

For stability of floating body M lies above G GM $\gt$ 0

Q3GATE 2011MCQ

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

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Q4GATE 2001MCQ

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

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