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 _____________

The absolute ratio of the net magnitude of vertical forces to the net magnitude of horizontal forces (round off to two decimal places) is _____________

0.61 | |

1.22 | |

0.22 | |

0.94 |

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

metacentre lies above its centre of gravity | |

metacentre lies below its centre of gravity | |

metacentre coincides with its centre of gravity | |

centre of gravity is below its centre of buoyancy |

Question 2 Explanation:

For stability of floating body M lies above G

GM \gt 0

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

O does not coincide with the centre of mass of the displaced fluid | |

G coincides with the centre of mass of the displaced fluid | |

O lies below G | |

O lies above G |

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

8.24 | |

7.82 | |

7.64 | |

7.38 |

There are 4 questions to complete.