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.