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question_answer1)
The total weight of a piece of wood is 6 kg. In the floating state in water its \[\frac{1}{3}\] part remains inside the water. On this floating piece of wood what maximum weight is to be put such that the whole of the piece of wood is to be drowned in the water?
A)
15 kg done
clear
B)
14 kg done
clear
C)
10 kg done
clear
D)
12 kg done
clear
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question_answer2)
A vessel contains oil\[(density=0.8\text{ }gm/c{{m}^{3}})\] over mercury\[(density=13.6\text{ }gm/c{{m}^{3}})\]. A homogeneous sphere floats with half of its volume immersed in mercury and the other half in oil. The density of the material of the sphere in \[gm/c{{m}^{3}}\]is
A)
33 done
clear
B)
6.4 done
clear
C)
72 done
clear
D)
12.8 done
clear
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question_answer3)
In a hydraulic lift, compressed air exerts a force \[{{F}_{1}}\] on a small piston having a radius of 5 cm. This pressure is transmitted to a second piston of radius 15 cm. If the mass of the load to be lifted is 1350 kg, find the value of\[{{F}_{1}}\]? The pressure necessary to accomplish this task is
A)
\[1.4\times {{10}^{5}}Pa\] done
clear
B)
\[12\times {{10}^{5}}Pa\] done
clear
C)
\[1.9\times {{10}^{5}}Pa\] done
clear
D)
\[1.9Pa\] done
clear
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question_answer4)
The force acting on a window of area\[50cm\times 50cm\] of a submarine at a depth of 2000 m ill an ocean, interior of which is maintained at sea level atmospheric pressure is (Density of sea water\[={{10}^{3}}kg{{m}^{-3}},g=10m{{s}^{-2}}\] )
A)
\[{{10}^{6}}N\] done
clear
B)
\[5\times {{10}^{5}}N\] done
clear
C)
\[25\times {{10}^{6}}N\] done
clear
D)
\[5\times {{10}^{6}}N\] done
clear
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question_answer5)
A concrete sphere of radius R has a cavity of radius r which is packed with sawdust. The specific gravities of concrete and sawdust are respectively 2.4 and 0.3 for this sphere to float with its entire volume submerged under water. Ratio of mass of concrete to mass of sawdust will be
A)
8 done
clear
B)
4 done
clear
C)
3 done
clear
D)
zero done
clear
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question_answer6)
A cubical box is to be constructed with iron sheets 1 mm in thickness. What can be the minimum value of the external edge so that the cube does not sink in water? \[[{{\delta }_{iron}}=8000kg/{{m}^{3}},{{\delta }_{water}}=1000kg/{{m}^{3}}]\]
A)
4.8cm done
clear
B)
5.8cm done
clear
C)
6.9 on done
clear
D)
7.3cm done
clear
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question_answer7)
The pressure at the bottom of a tank containing a liquid does not depend on
A)
Acceleration due to gravity done
clear
B)
Height of the liquid column done
clear
C)
Area of the bottom surface done
clear
D)
Nature of the liquid done
clear
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question_answer8)
A body B is capable of remaining stationary inside a liquid at the position shown in Fig. (a). If the whole system is gently placed on smooth inclined plane (Fig (b)) and is allowed to slide down, then (\[0<\theta <{{90}^{o}}\]). The body will
A)
Move up (relative to liquid) done
clear
B)
Move down (relative to liquid) done
clear
C)
Remain stationary (relative to liquid) done
clear
D)
Move up for some inclination \[\theta \] and will move down for another inclination \[\theta \] done
clear
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question_answer9)
A hollow sphere of mass \[M=50kg\]and radius\[r={{\left( \frac{3}{40\pi } \right)}^{1/3}}\]m is immersed in a tank of water (density \[{{\rho }_{w}}={{10}^{3}}kg/{{m}^{3}}\]). The sphere is tied to the bottom of a tank by two wires A and B as shown. Tension in wire A is\[(g=10m/{{s}^{2}})\]
A)
\[125\sqrt{2}N\] done
clear
B)
\[125N\] done
clear
C)
\[250\sqrt{2}N\] done
clear
D)
\[250N\] done
clear
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question_answer10)
In rising from the bottom of a lake, to the top, the temperature of an air bubble remains unchanged, but its diameter gets doubled. If h is the barometric height (expressed in m of mercury of relative density p) at the surface of the lake, the depth of the lake is
A)
\[8\text{ }\rho hm\] done
clear
B)
\[\text{7 }\rho hm\] done
clear
C)
\[\text{9 }\rho hm\] done
clear
D)
\[\text{12 }\rho hm\] done
clear
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question_answer11)
A hemispherical portion of radius R is removed from the bottom of a cylinder of radius R. The volume of the remaining cylinder is T and its mass M. It is suspended by a string in a liquid of density p where it stays vertical. The upper surface of the cylinder is at a depth h below the liquid surface. The force on the bottom of the cylinder by the liquid is
A)
\[Mg\] done
clear
B)
\[Mg-V\rho g\] done
clear
C)
\[Mg+\pi {{R}^{2}}h\rho g\] done
clear
D)
\[\rho g(V+\pi {{R}^{2}}h)\] done
clear
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question_answer12)
A thin tube sealed at both ends is 100 cm long. It lies horizontally, the middle 20 cm containing mercury and two equal ends containing air at standard atmospheric pressure. If the tube is now fumed to a vertical position, by what amount will the mercury be displaced? (Given: cross-section of the tube can be assumed to be uniform)
A)
2.95cm done
clear
B)
5.18cm done
clear
C)
8.65cm done
clear
D)
0.0cm done
clear
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question_answer13)
A right circular cone of density p, floats just immersed with its vertex downwards in a vessel containing two liquids of densities \[{{\rho }_{1}}\]and \[{{\rho }_{2}}\] respectively, the planes of separation of the two liquids cuts off from the axis of the cone a fraction z of its length. Find z.
A)
\[{{\left( \frac{\rho +{{\sigma }_{2}}}{{{\sigma }_{1}}+{{\sigma }_{2}}} \right)}^{1/3}}\] done
clear
B)
\[{{\left( \frac{\rho -{{\sigma }_{2}}}{{{\sigma }_{1}}-{{\sigma }_{2}}} \right)}^{1/3}}\] done
clear
C)
\[{{\left( \frac{\rho -{{\sigma }_{2}}}{{{\sigma }_{1}}+{{\sigma }_{2}}} \right)}^{1/2}}\] done
clear
D)
\[{{\left( \frac{\rho -{{\sigma }_{2}}}{{{\sigma }_{1}}-{{\sigma }_{2}}} \right)}^{1/2}}\] done
clear
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question_answer14)
A sphere of solid material of specific gravity 8 has a concentric spherical cavity and just sinks in water. The ratio of radius of cavity to that of outer radius of the sphere must be
A)
\[\frac{{{7}^{1/3}}}{2}\] done
clear
B)
\[\frac{{{5}^{1/3}}}{2}\] done
clear
C)
\[\frac{{{9}^{1/3}}}{2}\] done
clear
D)
\[\frac{{{3}^{1/3}}}{2}\] done
clear
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question_answer15)
A vessel containing water is given a constant acceleration 'a? towards the right along a straight horizontal path. Which of the following diagrams represents the surface of the liquid?
A)
B)
C)
D)
None of these done
clear
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question_answer16)
An iceberg is floating in ocean. What fraction of its volume is above the water? (Given: density of ice\[=900kg/{{m}^{3}}\] and density of ocean water \[=1030kg/{{m}^{3}}\])
A)
\[\frac{90}{103}\] done
clear
B)
\[\frac{13}{103}\] done
clear
C)
\[\frac{10}{103}\] done
clear
D)
\[\frac{1}{103}\] done
clear
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question_answer17)
A cone fall of water, is placed on its side on a horizontal table, the thrust on its base is x times the weight of the contained fluid, where 2a is the vertical angle of the cone. Find the value of x.
A)
\[3\cos \,\alpha \] done
clear
B)
\[3\sin \,\alpha \] done
clear
C)
\[2\sin \,\alpha \] done
clear
D)
\[2\cos \,\alpha \] done
clear
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question_answer18)
What is the absolute pressure of the gas above the liquid surface in the tank shown in fig. Density of \[oil=820kg/{{m}^{3}}\], density of mercury\[=13.6\times {{10}^{3}}kg/{{m}^{3}}\] Given 1 atmospheric pressure\[=1.01\times {{10}^{5}}N/{{m}^{2}}\]
A)
\[3.81\times {{10}^{5}}N/{{m}^{2}}\] done
clear
B)
\[6\times {{10}^{6}}N/{{m}^{2}}\] done
clear
C)
\[5\times {{10}^{7}}N/{{m}^{2}}\] done
clear
D)
\[4.6\times {{10}^{2}}N/{{m}^{2}}\] done
clear
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question_answer19)
Figure shows a U-tube of uniform cross-sectional area A, accelerated with acceleration a as shown. If d is the separation between the limbs, then what is the difference in the levels of the liquid in the U-tube is
A)
\[\frac{ad}{g}\] done
clear
B)
\[\frac{ag}{d}\] done
clear
C)
\[\frac{a}{d}\] done
clear
D)
\[\frac{dg}{a}\] done
clear
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question_answer20)
The two thigh bones, each of cross-sectional area \[10\text{ }c{{m}^{2}}\]support the upper part of a human body of mass 40 kg. Estimate the average pressure sustained by the bones. Take \[g=10m/{{s}^{2}}\]
A)
\[2\times {{10}^{5}}N/{{m}^{2}}\] done
clear
B)
\[5\times {{10}^{4}}N/{{m}^{2}}\] done
clear
C)
\[2\times {{10}^{7}}N/{{m}^{2}}\] done
clear
D)
\[3\times {{10}^{6}}N/{{m}^{2}}\] done
clear
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question_answer21)
A hemispherical bowl just floats without sinking in a liquid of density\[1.2\times {{10}^{3}}kg/{{m}^{3}}\]. If outer diameter and the density of the bowl are 1 m and \[2\times {{10}^{4}}kg/{{m}^{3}}\]respectively then the inner diameter of the bowl will be
A)
0.94 m done
clear
B)
0.97 m done
clear
C)
0.98 m done
clear
D)
0.99 m done
clear
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question_answer22)
A uniform rod of density p is placed in a wide tank containing a liquid of density\[{{\rho }_{0}}({{\rho }_{0}}>\rho )\].The depth of liquid in the tank is half the length of the rod. The rod is in equilibrium, with its lower end resting on the bottom of the tank. In this position the rod makes an angle 9 with the horizontal, then:
A)
\[\sin \theta =\frac{1}{2}\sqrt{{{\rho }_{0}}/\rho }\] done
clear
B)
\[\sin \theta =\frac{1}{2},\frac{{{\rho }_{0}}}{\rho }\] done
clear
C)
\[\sin \theta =\sqrt{\rho /{{\rho }_{0}}}\] done
clear
D)
\[\sin \theta ={{\rho }_{0}}/\rho \] done
clear
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question_answer23)
A solid sphere of density \[\eta (>1)\] times lighter than water is suspended in a water tank by a string tied to its base as shown in fig. If the mass of the Sphere is/w, then the tension in the string is given by
A)
\[\left( \frac{\eta -1}{\eta } \right)mg\] done
clear
B)
\[\eta mg\] done
clear
C)
\[\frac{mg}{\eta -1}\] done
clear
D)
\[(\eta -1)mg\] done
clear
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question_answer24)
A boy can reduce the pressure in his lungs to 750 mm of mercury. Using a straw he can drink water from a glass upto the maximum depth of (atmospheric pressure\[=760\text{ }mm\]of mercury; density of mercury\[=13.6gc{{m}^{-3}}\])
A)
13.6 cm done
clear
B)
9.8 cm done
clear
C)
10cm done
clear
D)
76cm done
clear
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question_answer25)
A wooden block, with a coin placed on its top, floats in water as shown in fig. the distance 1 and h are shown there. After some time the coin falls into the water. Then
A)
\[\ell \]decreases and h increases done
clear
B)
\[\ell \]increases and h decreases done
clear
C)
Both \[\ell \]and h increases done
clear
D)
Both \[\ell \] and h decreases done
clear
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question_answer26)
The density p of water of bulk modulus B at a depth y in the ocean is related to the density at surface\[{{\rho }_{0}}\] by the relation
A)
\[\rho ={{\rho }_{0}}\left[ 1-\frac{{{\rho }_{0}}gy}{B} \right]\] done
clear
B)
\[\rho ={{\rho }_{0}}\left[ 1+\frac{{{\rho }_{0}}gy}{B} \right]\] done
clear
C)
\[\rho ={{\rho }_{0}}\left[ 1+\frac{B}{{{\rho }_{0}}hgy} \right]\] done
clear
D)
\[\rho ={{\rho }_{0}}\left[ 1-\frac{B}{{{\rho }_{0}}hgy} \right]\] done
clear
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question_answer27)
Two non-mixing liquids of densities \[\rho \] and n\[\rho \] \[(n>1)\] are put in a container. The height of each liquid is h. A solid cylinder of length L and density d is put in this container. The cylinder floats with its axis vertical and length \[pL(p<1)\]in the denser liquid. The density d is equal to:
A)
\[\left\{ l+\left( n+l \right)p \right\}\rho ~~\] done
clear
B)
\[~\left\{ 2+\left( n+1 \right)p \right\}\rho \] done
clear
C)
\[\left\{ 2+\left( n-1 \right)p \right\}\rho \] done
clear
D)
\[\left\{ l+\left( n-1 \right)p \right\}\rho \] done
clear
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question_answer28)
Two wooden blocks A and B float in a liquid of density \[{{\rho }_{L}}\]as shown. The distance L and H are shown. After some time, block B falls into the liquid, so that L decreases and H increases. If density of block B is\[{{\rho }_{B}}\], find the correct option.
A)
\[{{\rho }_{_{L}}}={{\rho }_{B}}\] done
clear
B)
\[{{\rho }_{_{L}}}>{{\rho }_{B}}\] done
clear
C)
\[{{\rho }_{_{L}}}<{{\rho }_{B}}\] done
clear
D)
unpredictable done
clear
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question_answer29)
A homogeneous solid cylinder of length L (\[L<H/2\]), cross-sectional area \[A/5\] is immersed such that it floats with its axis vertical at the liquid- liquid interface with length \[L/4\] in the denser liquid as shown in the figure. The lower density liquid is open to atmosphere having pressure\[{{P}_{0}}\]. Then density D of solid is given by
A)
\[\frac{5}{4}d\] done
clear
B)
\[\frac{d}{4}\] done
clear
C)
\[4d\] done
clear
D)
\[\frac{d}{5}\] done
clear
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question_answer30)
The compressibility of water is \[4\times {{10}^{-5}}\]per unit atmospheric pressure. The decrease in volume of \[100c{{m}^{2}}\] water under a pressure of 100 atmosphere will be
A)
\[0.4c{{m}^{3}}\] done
clear
B)
\[4\times {{10}^{-5}}c{{m}^{3}}\] done
clear
C)
\[0.025c{{m}^{3}}\] done
clear
D)
\[0.004c{{m}^{3}}\] done
clear
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question_answer31)
A hollow wooden cylinder of height A, inner radius R and outer radius 2R is placed in a cylindrical container of radius 3R. When water is poured into the container, the minimum height H of the container for which cylinder can float inside freely is
A)
\[\frac{h{{p}_{water}}}{{{\rho }_{water}}+{{\rho }_{wood}}}\] done
clear
B)
\[\frac{h{{\rho }_{wood}}}{{{\rho }_{water}}}\] done
clear
C)
h done
clear
D)
\[\frac{{{h}^{2}}}{R}\] done
clear
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question_answer32)
A balloon of volume F, contains a gas whose density is to that of the air at the earth's surface as 1:15. If the envelope of the balloon be of weight w but of negligible volume, find the acceleration with which it will begin to ascend.
A)
\[\left( \frac{7Vg\sigma -w}{Vg\sigma +w} \right)\times g\] done
clear
B)
\[\left( \frac{2Vg\sigma -w}{Vg\sigma +w} \right)\times g\] done
clear
C)
\[\left( \frac{14Vg\sigma -w}{Vg\sigma +w} \right)\times g\] done
clear
D)
\[\left( \frac{14Vg\sigma +w}{Vg\sigma -w} \right)\times g\] done
clear
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question_answer33)
A uniform wooden stick of length L, cross- section area A and density d is immersed in a liquid of density 4rf. A small body of mass m and negligible volume is attached at the lower end of the rod so that the stick floats vertically in stable equilibrium then
A)
\[m>dAL\] done
clear
B)
\[m<dAL\] done
clear
C)
\[m<dAL/2\] done
clear
D)
\[m<dAL/4\] done
clear
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question_answer34)
Streamline flow is more likely for liquids with
A)
High density and low viscosity done
clear
B)
Low density and high viscosity done
clear
C)
High density and high viscosity done
clear
D)
Low density and low viscosity done
clear
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question_answer35)
In the arrangement as shown,\[{{m}_{B}}=3m\], density of liquid is r and density of block B is v. The system is released from rest so that block B moves up when in liquid and moves down when out of liquid with the same acceleration. Find the mass of block A.
A)
\[\frac{7}{4}m\] done
clear
B)
\[2m\] done
clear
C)
\[\frac{9}{2}m\] done
clear
D)
\[\frac{9}{4}m\] done
clear
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question_answer36)
In Bernoulli's theorem which of the following is conserved?
A)
Mass done
clear
B)
Linear momentum done
clear
C)
Energy done
clear
D)
Angular momentum done
clear
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question_answer37)
Water flows through a frictionless tube with a varying cross-section as shown in fig. Pressure P at points along the axis is represented by
A)
B)
C)
D)
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question_answer38)
Air flows horizontally with a speed\[v=106km/hr\] A house has plane roof of area\[A=20{{m}^{2}}\]. The magnitude of aerodynamic lift of the roof is
A)
\[1.127\times {{10}^{4}}N\] done
clear
B)
\[5.0\times {{10}^{4}}N\] done
clear
C)
\[1.127\times {{10}^{5}}N\] done
clear
D)
\[3.127\times {{10}^{4}}N\] done
clear
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question_answer39)
A wind with speed 40 m/s blows parallel to the roof of a house. The area of the roof is\[250{{m}^{2}}\]. Assuming that the pressure inside the house is atmospheric pressure, the force exerted by the wind on the roof and the direction of the force will be(\[{{\rho }_{air}}=1.2kg/{{m}^{3}}\])
A)
\[4.8\times {{10}^{5}}N,upwards\] done
clear
B)
\[2.4\times {{10}^{5}}N,upwards\] done
clear
C)
\[2.4\times {{10}^{5}}N,downwards\] done
clear
D)
\[4.8\times {{10}^{5}}N,downwards\] done
clear
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question_answer40)
In the figure shown the velocity and pressure of the liquid at the cross section (2) are given by (If \[{{P}_{0}}\] is the atmospheric pressure).
A)
\[\sqrt{2hg,\,}{{P}_{0}}+\frac{\rho hg}{2}\] done
clear
B)
\[\sqrt{hg,\,}{{P}_{0}}+\frac{\rho hg}{2}\] done
clear
C)
\[\sqrt{\frac{hg}{2},}{{P}_{0}}+\frac{3\rho hg}{4}\] done
clear
D)
\[\frac{\sqrt{hg,}}{2}{{P}_{0}}-\frac{\rho hg}{4}\] done
clear
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question_answer41)
A cylindrical vessel contains a liquid of density\[\rho \] filled upto a height h. The uper surface of the liquid is in contact with a pistion of mass m and area of cross-section A. A small hole is drilled at the bottom of the vessel. (Neglect the viscous effects) The speed with which the liquid comes out of the hoe is:
A)
\[\sqrt{2}gh\] done
clear
B)
\[\sqrt{2}g\left( h+\frac{m}{\rho A} \right)\] done
clear
C)
\[\sqrt{g\left( h+\frac{m}{\rho A} \right)}\] done
clear
D)
\[\sqrt{g\left( h+\frac{2m}{\rho A} \right)}\] done
clear
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question_answer42)
A wide vessel with a small hole at the bottom is filled with water (density\[{{\rho }_{1}}\], height\[{{h}_{1}}\]) and kerosene (density\[{{\rho }_{2}}\], height\[{{h}_{2}}\]). Neglecting viscosity effects, the speed with which water flows out is :
A)
\[[2g{{({{h}_{1}}+{{h}_{2}})}^{1/2}}\] done
clear
B)
\[[2g{{({{h}_{1}}{{\rho }_{1}}+{{h}_{2}}{{\rho }_{2}}]}^{1/2}}\] done
clear
C)
\[{{[2g({{h}_{1}}+{{h}_{2}}({{\rho }_{2}}/{{\rho }_{1}}))]}^{1/2}}\] done
clear
D)
\[{{[2g({{h}_{1}}+{{h}_{2}}({{\rho }_{1}}/{{\rho }_{2}}))]}^{1/2}}\] done
clear
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question_answer43)
The cylindrical tube of a spray pump has radius, R, one end of which has n fine holes, each of radius r. If the speed of the liquid in the tube is V, the speed of the ejection of the liquid through the holes is :
A)
\[\frac{V{{R}^{2}}}{n{{r}^{2}}}\] done
clear
B)
\[\frac{V{{R}^{2}}}{{{n}^{3}}{{r}^{2}}}\] done
clear
C)
\[\frac{{{V}^{2}}R}{nr}\] done
clear
D)
\[\frac{V{{R}^{2}}}{{{n}^{2}}{{r}^{2}}}\] done
clear
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question_answer44)
A fluid is in streamline flow across a horizontal pipe of variable area of cross section. For this which of the following statements is correct?
A)
The velocity is minimum at the narrowest part of the pipe and the pressure is minimum at the widest part of the pipe done
clear
B)
The velocity is maximum at the narrowest part of the pipe and pressure is maximum at the widest part of the pipe done
clear
C)
Velocity and pressure both are maximum at the narrowest part of the pipe done
clear
D)
Velocity and pressure both are maximum at the widest part of the pipe done
clear
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question_answer45)
Oil is filled in a cylindrical container upto height 4m. A small hole of area 'p' is punched in the wall of the container at a height 1.52m from the bottom. The cross sectional area of the container is Q. If\[\frac{p}{q}=0.1\]then v is (where v is the velocity of oil coming out of the hole)
A)
\[5\sqrt{2}\] done
clear
B)
\[6\sqrt{3}\] done
clear
C)
\[8\sqrt{2}\] done
clear
D)
\[7\sqrt{5}\] done
clear
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question_answer46)
. A broad vessel with water stands on a smooth surface. The level of the water in the vessel is h. The vessel together with the water weighs G. The side wall of the vessel has at the bottom a plugged hole (with rounded edges) with an area A. At what coefficient of friction between the bottom and the surface will the vessel begin to move if the plug is removed?
A)
\[\frac{\rho ghA}{G}\] done
clear
B)
\[\frac{2\rho ghA}{G}\] done
clear
C)
\[\frac{\rho ghA}{2G}\] done
clear
D)
\[\frac{2\rho ghA}{3G}\] done
clear
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question_answer47)
For a fluid which is flowing steadily, the level in the vertical tubes is best represented by
A)
B)
C)
D)
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question_answer48)
For the arrangement shown in the figure, find the time interval in seconds after which the water jet ceases to cross the wall. Area of the cross section of the tank\[A=\sqrt{5}{{m}^{2}}\] and area of the orifice \[A=4c{{m}^{2}}\]. [Assume that the container remaining fixed]
A)
\[1000s\] done
clear
B)
\[2000s\] done
clear
C)
\[1500s\] done
clear
D)
\[500s\] done
clear
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question_answer49)
Air of density \[1.2kg{{m}^{-3}}\] is blowing across the horizontal wings of an aero plane in such a way that its speeds above and below the wings are \[150m{{s}^{-1}}\] and\[100m{{s}^{-1}}\], respectively. The pressure difference between the upper and lower sides of the wings, is
A)
\[60N{{m}^{-2}}\] done
clear
B)
\[180\,N{{m}^{-2}}\] done
clear
C)
\[7500N{{m}^{-2}}\] done
clear
D)
\[12500N{{m}^{-2}}\] done
clear
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question_answer50)
In the figure shown, a light container is kept on a horizontal rough surface of coefficient of friction \[\mu =\frac{Sh}{V}\]. A very small hole of area S is made at depth h. Water of volume V is filled in the container. The friction is not sufficient to keep the container at rest. The acceleration of the container initially is
A)
\[\frac{V}{Sh}g\] done
clear
B)
\[g\] done
clear
C)
Zero done
clear
D)
\[\frac{Sh}{V}g\] done
clear
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question_answer51)
An incompressible liquid flows through a horizontal tube as shown in the figure, Then the velocity V of the fluid is
A)
\[3.0m/s\] done
clear
B)
\[1.5m/s\] done
clear
C)
\[1.0m/s\] done
clear
D)
\[2.25m/s\] done
clear
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question_answer52)
.. Figure shows a liquid flowing through a tube at the rate of\[0.1{{m}^{3}}/s\]. The tube is branched into two semicircular tubes of cross - sectional area A/3 and 2A/3, The velocity of liquid at Q is (the cross-section of the main tube is\[A={{10}^{-2}}{{m}^{2}}\] and \[{{V}_{p}}=20m/s\]
A)
5 m/s done
clear
B)
30m/s done
clear
C)
35 m/s done
clear
D)
None of these done
clear
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question_answer53)
A large tank filled with water to a height 'A' is to be emptied through a small hole at the bottom. The ratio of time taken for the level of water to fall from h to\[\frac{h}{2}\]and \[\frac{h}{2}\]to zero is
A)
\[\sqrt{2}\] done
clear
B)
\[\frac{1}{\sqrt{2}}\] done
clear
C)
\[\sqrt{2}-1\] done
clear
D)
\[\frac{1}{\sqrt{2}-1}\] done
clear
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question_answer54)
A square box of water has a small hole located in one of the bottom comer. When the box is fall and sitting on a level surface, complete opening of the whole results in a flow of water with a speed\[{{v}_{0}}\], as shown in figure. When the box is half empty, it is tilted by \[45{}^\circ \] so that the hole is at the lowest point. Now the water will flow out with a speed of
A)
\[{{v}_{0}}\] done
clear
B)
\[{{v}_{0}}/2\] done
clear
C)
\[{{v}_{0}}/\sqrt{2}\] done
clear
D)
\[{{v}_{0}}/\sqrt[4]{2}\] done
clear
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question_answer55)
A horizontal tube has different cross sections at points A and B. The area of cross section are \[{{a}_{1}}\]and\[{{a}_{2}}\], respectively, and pressures at these points are \[{{p}_{1}}=\rho g{{h}_{1}}\]and\[{{p}_{2}}=\rho g{{h}_{2}}\], where p is the density of liquid flowing in the tube and \[{{h}_{1}}\]and \[{{h}_{2}}\]are heights of liquid columns in vertical tubes connected at A and B. If\[{{h}_{1}}-{{h}_{2}}=h\], then the flow rate of the liquid in the horizontal tube is
A)
\[{{a}_{1}}{{a}_{2}}\sqrt{\frac{2gh}{a_{1}^{2}-a_{2}^{2}}}\] done
clear
B)
\[{{a}_{1}}{{a}_{2}}\sqrt{\frac{2g}{h\left( a_{1}^{2}-a_{2}^{2} \right)}}\] done
clear
C)
\[{{a}_{1}}{{a}_{2}}\sqrt{\frac{(a_{1}^{2}+a_{2}^{2})h}{2g\left( a_{1}^{2}-a_{2}^{2} \right)}}\] done
clear
D)
\[\frac{2{{a}_{1}}{{a}_{2}}gh}{\sqrt{a_{1}^{2}-a_{2}^{2}}}\] done
clear
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question_answer56)
. Water is filled in a cylindrical container to a height of 3m. The ratio of the cross-sectional area of the orifice and the beaker is 0.1. The square of the speed of the liquid coming out from the orifice is (\[g=10m/{{s}^{2}}\])
A)
\[50{{m}^{2}}/{{s}^{2}}\] done
clear
B)
\[50.5{{m}^{2}}/{{s}^{2}}\] done
clear
C)
\[51{{m}^{2}}/{{s}^{2}}\] done
clear
D)
\[52{{m}^{2}}/{{s}^{2}}\] done
clear
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question_answer57)
Water is flowing through a horizontal tube having cross-sectional areas of its two ends being A and A' such that the ratio A/A' is 5. If the pressure difference of water between the two ends is\[3\times {{10}^{5}}\text{ }N{{m}^{-2}}\], the velocity of water with which it enters the tube will be (neglect gravity effects)
A)
\[5m{{s}^{-1}}\] done
clear
B)
\[10m{{s}^{-1}}\] done
clear
C)
\[25\,m{{s}^{-1}}\] done
clear
D)
\[50\sqrt{10}\,m{{s}^{-1}}\] done
clear
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question_answer58)
There are two identical small holes P and Q of area of cross-section a on the opposite sides of a tank containing a liquid of density p. The difference in height between the holes is h. Tank is resting on a smooth horizontal surface. Horizontal force which will has to be applied on the tank to keep it in equilibrium is
A)
\[gh\rho a\] done
clear
B)
\[\frac{2gh}{\rho a}\] done
clear
C)
\[2\rho agh\] done
clear
D)
\[\frac{\rho gh}{a}\] done
clear
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question_answer59)
In a cylindrical water tank, there are two small holes A and B on the wall at a depth of\[{{h}_{1}}\], from the surface of water and at a height of\[{{h}_{2}}\] from the bottom of water tank. Surface of water is at height of \[{{h}_{2}}\] from the bottom of water tank. Surface of water is at height H from the bottom of water tank. Water coming out from both holes strikes the ground at the same point S. Find the ratio of\[{{h}_{1}}\] and \[{{h}_{2}}\]
A)
Depends on H done
clear
B)
\[1:1\] done
clear
C)
\[2:2\] done
clear
D)
\[1:2\] done
clear
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question_answer60)
Equal volumes of two immiscible liquids of densities \[\rho \] and \[2\rho \] are filled in a vessel as shown in figure. Two small holes are punched at depth \[h/2\]and \[3h/2\] from the surface of lighter liquid. If\[{{v}_{1}}\] and \[{{v}_{2}}\] are the velocities of a flux at these two holes, then \[{{v}_{1}}/{{v}_{2}}\]is
A)
\[\frac{1}{2\sqrt{2}}\] done
clear
B)
\[\frac{1}{2}\] done
clear
C)
\[\frac{1}{4}\] done
clear
D)
\[\frac{1}{\sqrt{2}}\] done
clear
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question_answer61)
A tank with a small hole at the bottom has been filled with water and kerosene (specific gravity 0.8). The height of water is 3m and that of kerosene 2m. When the hole is opened the velocity of fluid coming out from it is nearly: (take \[g=10m{{s}^{-2}}\]and density of water\[={{10}^{3}}kg{{m}^{-3}}\])
A)
\[10.7\,m{{s}^{-1}}\] done
clear
B)
\[9.8\,m{{s}^{-1}}\] done
clear
C)
\[8.5\,m{{s}^{-1}}\] done
clear
D)
\[7.6\,m{{s}^{-1}}\] done
clear
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question_answer62)
If it takes 5 minutes to fill a 15 litre bucket from a water tap of diameter\[\frac{2}{\sqrt{\pi }}cm\] then the Reynold's number for the flow is close to: (density of water\[={{10}^{3}}\,kg/{{m}^{3}}\] and viscosity of water\[={{10}^{-3}}Pa.s\])
A)
1100 done
clear
B)
11,000 done
clear
C)
550 done
clear
D)
5500 done
clear
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question_answer63)
Water is flowing on a horizontal fixed surface, such that its flow velocity varies with y (vertical direction) as\[v=k\left( \frac{2{{y}^{2}}}{{{a}^{2}}}-\frac{{{y}^{3}}}{{{a}^{3}}} \right)\]. If coefficient of viscosity for water is\[\eta \], what will be shear stress between layers of water at\[y=a.\]
A)
\[\frac{\eta k}{a}\] done
clear
B)
\[\frac{\eta }{ka}\] done
clear
C)
\[\frac{\eta a}{k}\] done
clear
D)
None of these done
clear
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question_answer64)
A container filled with viscous liquid is moving vertically downwards with constant speed\[3{{v}_{0}}\]. At the instant shown, a sphere of radius r is moving vertically downwards (in liquid) has speed\[{{v}_{0}}\]. The coefficient of viscosity is\[\eta \]. There is no relative motion between the liquid and the container. Then at the shown instant, the magnitude of viscous force acting on sphere is
A)
\[6\pi \eta r{{v}_{0}}\] done
clear
B)
\[12\pi \eta r{{v}_{0}}\] done
clear
C)
\[18\pi \eta r{{v}_{0}}\] done
clear
D)
\[24\pi \eta r{{v}_{0}}\] done
clear
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question_answer65)
As the temperature of a liquid is raised, the coefficient of viscosity
A)
Decreases done
clear
B)
Increases done
clear
C)
Remains the same done
clear
D)
May increase or decrease depending on the nature of liquid done
clear
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question_answer66)
After terminal velocity is reached, the acceleration of a body falling through a fluid is
A)
Equal to g done
clear
B)
zero done
clear
C)
Less than g done
clear
D)
greater than g done
clear
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question_answer67)
An air bubble of radius 1 cm rises with terminal velocity 0.21 cm/s in liquid column. If the density of liquid is\[1.47\times {{10}^{3}}kg/{{m}^{3}}\]. Then the value of coefficient of viscosity of liquid ignoring the density of air, will be
A)
\[1.71\times {{10}^{4}}poise\] done
clear
B)
\[1.82\times {{10}^{4}}poise\] done
clear
C)
\[1.78\times {{10}^{4}}poise\] done
clear
D)
\[1.52\times {{10}^{4}}poise\] done
clear
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question_answer68)
The relative velocity of two parallel layers of water is 8 cm/sec. If the perpendicular distance between the layers is 0.1 cm. Then velocity gradient will be
A)
80/sec done
clear
B)
60/sec done
clear
C)
50/sec done
clear
D)
40/sec done
clear
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question_answer69)
If a ball of steel (density\[\rho =7.8g\,c{{m}^{-3}}\]) attains a terminal velocity of \[10cm{{s}^{-1}}\] when falling in a tank of water (coefficient of viscosity \[{{\eta }_{water}}=8.5\times {{10}^{-4}}Pa-s\]) then its terminal velocity in glycerin(\[\rho =12gc{{m}^{-3}},\,\eta =13.2Pa-s\]) would be nearly
A)
\[1.6\times {{10}^{-5}}cm{{s}^{-1}}\] done
clear
B)
\[6.25\times {{10}^{-4}}cm{{s}^{-1}}\] done
clear
C)
\[6.45\times {{10}^{-4}}cm{{s}^{-1}}\] done
clear
D)
\[1.5\times {{10}^{-5}}cm{{s}^{-1}}\] done
clear
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question_answer70)
What is the velocity v of a metallic ball of radius r falling in a tank of liquid at the instant when its acceleration is one -half that of a freely falling body? (The densities of metal and of liquid are \[\rho \] and \[\sigma \] respectively, and the viscosity of the liquid is \[\eta \]).
A)
\[\frac{{{r}^{2}}g}{9\eta }(\rho -2\sigma )\] done
clear
B)
\[\frac{{{r}^{2}}g}{9\eta }(2\rho -\sigma )\] done
clear
C)
\[\frac{{{r}^{2}}g}{9\eta }(\rho -\sigma )\] done
clear
D)
\[\frac{2{{r}^{2}}g}{9\eta }(\rho -\sigma )\] done
clear
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question_answer71)
A spherical ball of iron of radius 2 mm is falling through a column of glycerine. If densities of glycerine and iron are respectively \[1.3\times {{10}^{3}}kg/{{m}^{3}}\]and\[8\times {{10}^{3}}kg/{{m}^{3}}\].\[\eta \]for glycerine \[=0.83N{{m}^{-2}}\sec \], then the terminal velocity is
A)
0.7 m/s done
clear
B)
0.07 m/s done
clear
C)
0.007 m/s done
clear
D)
0.0007 m/s done
clear
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question_answer72)
A small spherical ball falling through a viscous medium of negligible density has terminal velocity v. Another ball of the same mass but of radius twice that of the earlier falling through the same viscous medium will have terminal velocity
A)
v done
clear
B)
v/4 done
clear
C)
v/2 done
clear
D)
2v done
clear
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question_answer73)
The velocity of water in a river is 18 km/hr near the surface. If the river is 5m deep, find the shearing stress between the horizontal layers of water. The co-efficient of viscosity of water\[={{10}^{-2}}poise\].
A)
\[{{10}^{-1}}N/{{m}^{2}}\] done
clear
B)
\[{{10}^{-2}}N/{{m}^{2}}\] done
clear
C)
\[{{10}^{-3}}N/{{m}^{2}}\] done
clear
D)
\[{{10}^{-4}}N/{{m}^{2}}\] done
clear
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question_answer74)
A rain drop of radius 0.3mm falling vertically downwards in air has a terminal velocity of 1 m/ s. The viscosity of air is\[18\times {{10}^{-5}}poise\]. The viscous force on the drop is
A)
\[101.73\times {{10}^{-4}}dyne\] done
clear
B)
\[101.73\times {{10}^{-5}}dyne\] done
clear
C)
\[16.95\times {{10}^{-5}}dyne\] done
clear
D)
\[16.95\times {{10}^{-4}}dyne\] done
clear
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question_answer75)
The average mass of rain drops is\[3.0\times {{10}^{-5}}kg\] and their average terminal velocity is 9 m/s. Calculate the energy transferred by rain to each square metre of the surface at a place which receives 100 cm of rain in a year.
A)
\[3.5\times {{10}^{5}}J\] done
clear
B)
\[4.05\times {{10}^{4}}J\] done
clear
C)
\[3.0\times {{10}^{5}}J\] done
clear
D)
\[9.0\times {{10}^{4}}J\] done
clear
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question_answer76)
Which of the following is the velocity time graph of a small spherical body falling through a long columns of a viscous liquid?
A)
B)
C)
D)
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question_answer77)
A certain number of spherical drops of a liquid of radius 'r' coalesce to form a single drop of radius 'R' and volume 'V'. If 'T' is the surface tension of the liquid, then:
A)
\[energy=4VT\text{ }\left( \frac{1}{r}-\frac{1}{R} \right)\text{ }is\text{ }released\] done
clear
B)
\[energy\text{ }=3VT\text{ }\left( \frac{1}{r}+\frac{1}{R} \right)is\text{ }absorbed\] done
clear
C)
\[energy\text{ }=\text{ }3VT\left( \frac{1}{r}-\frac{1}{R} \right)is\text{ }released\] done
clear
D)
Energy is neither released nor absorbed done
clear
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question_answer78)
A soap film of surface tension \[3\times {{10}^{-2}}\] formed in a rectangular frame cam support a straw as shown in Fig. If \[g=10m{{s}^{-12}}\], the mass of the straw is
A)
0.006g done
clear
B)
0.06 g done
clear
C)
0.6 g done
clear
D)
6g done
clear
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question_answer79)
Two soap bubbles of radii a and b combine to form a single bubble of radius c. If P is the external pressure, then the surface tension of the soap solution is
A)
\[\frac{P({{c}^{3}}+{{a}^{3}}+{{b}^{3}})}{4({{a}^{2}}+{{b}^{2}}-{{c}^{2}})}\] done
clear
B)
\[\frac{P({{c}^{3}}-{{a}^{3}}-{{b}^{3}})}{4({{a}^{2}}+{{b}^{2}}-{{c}^{2}})}\] done
clear
C)
\[P{{c}^{3}}-4{{a}^{2}}-4{{b}^{2}}\] done
clear
D)
\[P{{c}^{3}}-2{{a}^{2}}-3{{b}^{2}}\] done
clear
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question_answer80)
Drops of liquid of density p are floating half immersed in a liquid of density a. If the surface tension of liquid is T, the radius of the drop will be
A)
\[\sqrt{\frac{3T}{g(3\rho -\sigma )}}\] done
clear
B)
\[\sqrt{\frac{6T}{g(2\rho -\sigma )}}\] done
clear
C)
\[\sqrt{\frac{3T}{g(2\rho -\sigma )}}\] done
clear
D)
\[\sqrt{\frac{3T}{g(4\rho -3\sigma )}}\] done
clear
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question_answer81)
A soap bubble of radius R is surrounded by another soap bubble of radius 2R, as shown. Take surface tension\[=S\]. Then the pressure inside the smaller soap bubble, in excess of the atmospheric pressure, will be
A)
4S/R done
clear
B)
3S/R done
clear
C)
6S/R done
clear
D)
None of these done
clear
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question_answer82)
Two spherical bubbles are in contact with each other internally as shown. The radius of curvature of the common surface is R, then
A)
\[R>{{R}_{1}}\] done
clear
B)
\[{{R}_{1}}>R>{{R}_{2}}\] done
clear
C)
\[R<{{R}_{2}}\] done
clear
D)
\[R={{R}_{1}}\] done
clear
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question_answer83)
Water of density p in a clean aquarium forms a meniscus, as illustrated in the figure. Calculate the difference in height h between the centre and the edge of the meniscus. The surface tension of water is\[\gamma \].
A)
\[\sqrt{\frac{2\gamma }{\rho g}}\] done
clear
B)
\[\sqrt{\frac{\gamma }{\rho g}}\] done
clear
C)
\[\frac{1}{2}\sqrt{\frac{\gamma }{\rho g}}\] done
clear
D)
\[2\sqrt{\frac{\gamma }{\rho g}}\] done
clear
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question_answer84)
The lower end of a capillary tube of radius 2.00mm is dipped 10.00cm below the surface of water in a beaker. Calculate the pressure within a bubble blown at its end in water, in excess of atmospheric pressure. [Surface tension of water\[72\times {{10}^{-3}}N/m\]]
A)
\[718N{{m}^{-2}}\] done
clear
B)
\[912N{{m}^{-2}}\] done
clear
C)
\[1160N{{m}^{-2}}\] done
clear
D)
\[1052N{{m}^{-2}}\] done
clear
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question_answer85)
A water film is formed between two straight parallel wires of 10 cm length 0.5 cm apart. If the distance between wires is increased by 1 mm. What will be the work done? (surface tension of water \[=72dyne/cm\] )
A)
36 erg done
clear
B)
288 erg done
clear
C)
144 erg done
clear
D)
72 erg done
clear
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question_answer86)
A vertical capillary tube with inside diameter 0.5mm is submerged into water so that the length of its part protruding over the surface of water is equal to 2.5mm. Find the radius of curvature of the meniscus.
A)
0.3mm done
clear
B)
0.6mm done
clear
C)
0.9mm done
clear
D)
1.2mm done
clear
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question_answer87)
A large number of droplets, each of radius, r coalesce to form a bigger drop of radius, R. An engineer designs a machine so that the energy released in this process is converted into the kinetic energy of the drop. Velocity of the drop is (\[T=\]surface tension, \[\rho =\]density)
A)
\[{{\left[ \frac{T}{\rho }\left( \frac{1}{r}-\frac{1}{R} \right) \right]}^{1/2}}\] done
clear
B)
\[{{\left[ \frac{6T}{\rho }\left( \frac{1}{r}-\frac{1}{R} \right) \right]}^{1/2}}\] done
clear
C)
\[{{\left[ \frac{3T}{\rho }\left( \frac{1}{r}-\frac{1}{R} \right) \right]}^{1/2}}\] done
clear
D)
\[{{\left[ \frac{2T}{\rho }\left( \frac{1}{r}-\frac{1}{R} \right) \right]}^{1/2}}\] done
clear
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question_answer88)
An air bubble of radius 0.1 cm is in a liquid having surface tension 0.06 N/m and density\[{{10}^{3}}kg/{{m}^{2}}\]. The pressure inside the bubble is \[100N{{m}^{-2}}\] greater than the atmospheric pressure. At what depth is the bubble below the surface of the liquid? (\[g=9.8m{{s}^{-2}}\])
A)
1.1m done
clear
B)
0.15m done
clear
C)
0.20m done
clear
D)
0.25m done
clear
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question_answer89)
Radius of a capillary is\[2\times {{10}^{-3}}m\]. A liquid of weight \[6.28\times {{10}^{-4}}N\] may remain in the capillary then the surface tension of liquid will be
A)
\[5\times {{10}^{-3}}N/m\] done
clear
B)
\[5\times {{10}^{-2}}N/m\] done
clear
C)
\[5N/m\] done
clear
D)
\[50N/m\] done
clear
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question_answer90)
Two capillary of length L and 2L and of radius R and 2R are connected in series. The net rate of flow of fluid through them will be (given rate to the flow through single capillary, \[X=\frac{\pi P{{R}^{4}}}{8\eta L}\])
A)
\[\frac{8}{9}X\] done
clear
B)
\[\frac{9}{8}X\] done
clear
C)
\[\frac{5}{7}X\] done
clear
D)
\[\frac{7}{5}X\] done
clear
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