Question 1 |

A pressure measurement device fitted on the surface of a submarine, located at a depth H below the surface of an ocean, reads an absolute pressure of 4.2 MPa. The density of sea water is 1050 kg/m^3, the atmospheric pressure is 101 kPa, and the acceleration due to gravity is 9.8 m/s^2. The depth H is _______ m (round off to the nearest integer).

128 | |

398 | |

478 | |

256 |

Question 1 Explanation:

\begin{aligned} &P_{A}=4.2 \mathrm{MPa}\;\;\;\;\text { [Absolute pressure] }\\ P_{\text {atm }} &=101 \mathrm{kPa} \\ \rho &=1050 \mathrm{~kg} / \mathrm{m}^{3} \\ g &=9.8 \mathrm{~m} / \mathrm{s}^{2} \\ P_{A} &=P_{\text {atm }}+\rho \mathrm{gH} \\ 4.2 \times 10^{6} &=\left(101 \times 10^{3}\right)+[1050 \times 9.81 \times \mathrm{H}] \\ H &=397.94 \text { or } 398 \mathrm{~m} \end{aligned}

Question 2 |

In the space above the mercury column in a barometer tube, the gauge pressure of the
vapour is

positive, but more than one atmosphere | |

negative | |

zero | |

positive, but less than one atmosphere |

Question 2 Explanation:

In space above mercury column in barometer, ideally perfect vaccum is expected. But due to evaporation of mercury , the pressure in that space is equal to vapour pressure of mercury [nearly 0.2 Pa (abs)] . As absolute pressure in that space is less than atmospheric pressure, gauge pressure is negative.

Question 3 |

Which of the following conditions is used lo determine the stable equilibrium of all partially
submerged floating bodies?

Centre of buoyancy must be above the centre of gravity | |

Centre of buoyancy must be below the centre of gravity | |

Metacentre must be at a higher level than the centre of gravity | |

Metacentre must be at a lower level than the centre of gravity |

Question 3 Explanation:

Metacentre must be higher level than the centre of gravity

Question 4 |

For the stability of a floating body the

centre of buoyancy must coincide with the centre of gravity | |

centre of buoyancy must be above the centre of gravity | |

centre of gravity must be above the centre of buoyancy | |

metacenter must be above the centre of gravity |

Question 4 Explanation:

GM=BM-BG

(i) GM \gt 0, stable

(ii) GM = 0, Neutral

(iii) GM \gt 0, unstable

NOTE:: Metacentre (M) must always be above the centre of gravity.

Question 5 |

Consider a frictionless, massless and leak-proof plug blocking a rectangular hole of dimensions 2R x L at the bottom of an open tank as shown in the figure. The head of the plug has the shape of a semi-cylinder of radius R. The tank is filled with a liquid of density \rho up to the tip of the plug. The gravitational acceleration is g. Neglect the effect of the atmospheric pressure.

The force F required to hold the plug in its position

The force F required to hold the plug in its position

2\rho R^{2}gL\left( 1-\frac{\pi }{4}\right ) | |

2\rho R^{2}gL\left( 1+\frac{\pi }{4}\right ) | |

\pi R^{2}\rho gL | |

\frac{\pi }{2}\rho R^{2}gL |

Question 5 Explanation:

\begin{aligned} \text{Volume, } V_{total}&=2R \times L \times R\\ &=2R^2L\;\;...(i)\\ \text{Volume: }V_1&=\frac{1}{2}\times \pi R^2 \times L\;\;...(ii)\\ F&= \text{Weight of fluid}\\ &=[V_{total}-V_{1}]\rho g\\ &=\left [ 2R^2L-\frac{\pi R^2L}{2} \right ]\rho g\\ &=\left [ 1-\frac{\pi}{4} \right ]2R^2Lg\rho \\ &=2\rho R^2gL\left [ 1-\frac{\pi}{4} \right ] \end{aligned}

There are 5 questions to complete.

ANSWER FOR QN:20 IS B

WHY BECAUSE IN MOHR’S CIRCLE DIAGRAM NORMAL STRESS IS POINTED ON NEGATIVE X-AXIS.