394 + Interview Questions in MECHANICAL-PROPERTIES-OF-FLUIDS IN GENERAL AWARENESS Page 7 InterviewSolution

301.	A hollow metal sphere is found to float in water with the highest point just touching the free surface of water. If `d` is the density of the metal in cgs units, the fraction that represents the volume of the hollow in terms of the volume of the sphere isA. `(1)/(d)`B. `(1-(1)/(d))`C. `(d)/((d-1))`D. `(1+(1)/(d))`
Answer» Correct Answer - B `(V_("cavity"))/(V_(S))=(V_(S)-V_("metal"))/(V_(S))=1-(V_("metal"))/(V_(S))=1-(d_(W))/(d)`

Discussion

302.	The range of water flowing out of a small hole made at a depth `10 m` below water surface in a large tank is `R`. Find the extra pressure (in atm) applied on the water surface so that range becomes `2R`. Take `1atm=10^(5)Pa`.
Answer» Correct Answer - 3 `V=(2gh)^(1//2)` Range will be twice, if efflux velocity becomes twice or h becomes four times or 40 m extra pressure`=` 30m of water head but 1 atm `=0.7xx13.6m` of water `=10.336m` of water, `30m` of water `=3.0atm`.

Discussion

303.	An artery in a certain person has been widened `1(1)/(2)` times the original diamter. If the pressure difference across the artery is maintaned constant, the blood flow through the artery will be increased toA. `(3//2)` timesB. `(9//4)` timesC. no changeD. `(81//16)` times
Answer» Correct Answer - D `Q=(piPr^(4))/(8etal),Qalphar^(4)`

Discussion

304.	An ideal liquid is flowing in two pipes, AC is inclined and BD is horizontal. Both the pipes are connected by two vertical tubes of length `h_(1)` and `h_(2)` as shown in the fig. The flow is streamline in both the pipes. if velocity of liquid at A, B and C are `2m//s, 4m//s` and `4m//s` respectively, the velocity at D will beA. `4m//s`B. `sqrt(14)m//s`C. `sqrt(28)m//s`D. none
Answer» Correct Answer - C `P_(A)+(1)/(2)rhoV_(A)^(2)=P_(C)+(1)/(2)rhoV_(C)^(2)+rhog(h_(2)-h_(1))` `P_(A)-P_(C)=(1)/(2)rho(V_(C)^(2)-V_(A)^(2))+rhog(h_(2)-h_(1))` `P_(B)+(1)/(2)rhoV_(B)^(2)=P_(D)+(1)/(2)rhoV_(D)^(2)` `P_(A)+rhogh_(1)+(1)/(2)rhoV_(B)^(2)=P_(C)+rhogh_(2)+(1)/(2)rhoV_(D)^(2)` `P_(A)+(1)/(2)rhoV_(B)^(2)=P_(C)+rho(h_(2)-h_(1))+(1)/(2)rhoV_(D)^(2)` `(1)/(2)(V_(C)^(2)-V_(A)^(2))+rhog(h_(2)-h_(1))+(1)/(2)rhoV_(B)^(2)` `=rhog(h_(2)-h_(1))+(1)/(2)rhoV_(D)^(2)(1)/(2)xx12+(1)/(2)xx12+(1)/(2)xx16=(1)/(2)V_(D)^(2)`, `V_(D)=sqrt(28)(m)/(s)`

Discussion

305.	Water flows with a velocity V in a tube of diameter d and the rate of flow is Q. another tube of diameter 2d is coupled to the first one. The velocity of water flowing out and rate of flow in the second tube are respectively.A. `(V)/(4)` and `Q`B. `(V)/(2)` and `(Q)/(2)`C. `2V` and `2Q`D. `(V)/(2)` and `2Q`
Answer» Correct Answer - 1 `A_(1)v_(1)=A_(2)v_(2),V_(1)d_(1)^(2)=V_(2)d_(2)^(2)`

Discussion

306.	A metal block of area 0.10 `m^(2)` is connected to a 0.02 kg mass via a string. The string passes over an ideal pulley (considered massless and frictionless) as shown in figure. A liquid with a flim of thickness 0.15 mm is placed between the plate and the table. When released the plate movees to the right with a constant speed of 0.075 m `s^(-1)`. What is the coefficient of viscosity of the liquid?
Answer» Area of the film, A = 0.10 `m^(2)` Thickness of the film = 0.15 mm x = 0.25 `xx 10^(-3)`m Relative velocity of plate v = 0.075 m `s^(-1)` Since the plate moves with constant speed, the tension developed in the string is equal to the viscous force F. But tension is equal to the weight of suspended mass m. `therefore` Viscous force F = weight of mass = 0.02 `xx` 9.8 = 0.196 N `F = eta (Av)/(x)` `rArr eta = (Fx)/(Av)` `=(0.196 xx 0.15 xx 10^(-3))/(0.10 xx 0.075)` `=(0.0196)/(5)` = 0.00392 Pa s

Discussion

307.	The flow rate from a tap of diameter `1.25 cm` is `3` L//min. The coefficient of viscosity of water is `10^(-3)` pa-s. Characterize the flow.A. stream lineB. turbulent aC. a and bD. none
Answer» Correct Answer - 1 `R=(rhoVd)/(eta)`.

Discussion

308.	Estimate the speed of verticaly falingn raindriops from the following data. Radius of the drops=0.02cm, viscosity of ir `=1.8xx10^-4 poise, g=9.9xx10ms^2 and ` density of water =1000 kg m^-3`.
Answer» Correct Answer - 5 `v=(2)/(9)r^(2)g.((d-rho))/(eta)`

Discussion

309.	Water is flowing in a pipe of radius 1.5 cm with an average velocity 15 cm `s^(-1)`. What is the nature of flow? Given coefficient of viscosity of water is `10^(-3)` kg `m^(-1) s^(-1)` and its density is `10^(3)` kg `m^(-3)`
Answer» `R_(e) = (rho vD)/(eta)` Here `rho`, density = `10^(3)` kg `m^(-3)` Coeff. Of viscosity, `eta = 10^(-3)` kg `m^(-1) s^(-1)` Average velocity of water, v = 15 cm `s^(-1)` = 0.15 m `s^(-1)` Diameter of pipe, D = 2 `xx` 1.5 cm = 3 cm = 0.03 m Hence, `R_(e) = (10^(3) xx 0.15 xx 0.03)/(10^(-3))` = `10^(6) xx 0.0045` = 4500 `R_(e) gt 2000` Therefore, the flow is turbulent.

Discussion

310.	A liquid is flowing through a narrow tube. The coefficient of viscosity of liquid is 0.1308 poise. The length and inner radius of tube are 50 cm and 1 mm respectively. The rate of flow of liquid is `360(cm^(3))/(min)`. Find the pressure difference between ends of tube.A. `10^(6)("dyne")/(cm^(2))`B. `10^(4)("dyne")/(cm^(2))`C. `10("dyne")/(cm^(2))`D. none of these
Answer» Correct Answer - A `v=(ppir^(4))/(8etal)`

Discussion

311.	A jar filled with two non-mixing liquid 1 and 2 having densities `rho_(1)` and `rho_(2)` respectively. A solid ball, made of a material of density `rho_(3)` is dropped in the jar. It come to equilibrium in the position shown in the figure. Which of the following is true for `rho_(1),rho_(2)` and `rho_(3)`?A. `rho_(1) lt rho lt rho_(3)`B. `rho_(1) lt rho_(3) lt rho_(2)`C. `rho_(3) lt rho_(1) lt rho_(2)`D. `rho_(1) lt rho_(3) lt rho_(2)`
Answer» Correct Answer - B

Discussion

312.	The rise in the water level in a capillary tube of radius 0.07 cm when dipped veryically in a beaker containing water of surface tension `0.07 N m^(-1)` is (g = `10 m s^(-2)`)A. 2 cmB. 4 cmC. 1.5 cmD. 3 cm
Answer» Correct Answer - A Rise of a liquid in a capillary tube, `h=(2Scostheta)/(r rhog)` Here, r=0.07cm `= 0.07xx10^(-2)m` For water , `S=0.07 N m^(-1), rho=10^(3) kg m^(-3)` Angle of contact `theta=0^(@)` `therefore h=(2xx(0.07 N m^(-1))xx1)/((0.07xx10^(-2)m)(10^(3) kg m^(-3))(10 m s^(-2)))` `=2xx10^(-2)m=2` cm

Discussion

313.	A squre wire frame of side `L` is dipped in a liquid. On taking out , a membrane is formed if the surface tension of liquid is T, the force acting on the frame due to the membrane will beA. 2 TLB. 4 TLC. 8 TLD. 16 TL
Answer» Correct Answer - 3 For each wire force is `2Tl` so that for four wires of frame `F=8Tl`

Discussion

314.	Expression for the height of capillary rise between two parallel plates dipping liquid of density `sigma` separated by a distance d. The surface tension of the liquid is T. [Take angle of contact to be zero]A. `h=(2T)/(sigmadg)`B. `h=(2d)/(sigmaT)`C. `h=(sigmaT)/(d)`D. `h=(2T^(2))/(sigmad)`
Answer» Correct Answer - A The meniscus between two plates in cylindrical is shape. Pressure at A (the lowestpoint of the meniscus) `p_(A)=p_(0)-(T)/(r)` Pressure at `B=` pressure at `C=p_(0)=` pressure at `A+sigmagh` `becauseP_(B)=p_(0)=p_(0)-(T)/(r)+sigmagh,h=(T)/(sigmagr)=(2T)/(sigmagd)` Alternative method: Force upward `=2lTcostheta=2lT(becausetheta=0^(@))` Gravitational pull `=("Volume"xx"density")g=lhdsigmag` `because2lT=lhdrhogimpliesh=(2T)/(dsigmag)`

Discussion

315.	Find the attractive force is newton between two parallel glass plates, separated by a distance `h=0.1mm` after a water drop of mass `m=70mg` was introduced between them. Assume wetting to be complete and surface tensin of water, `T=70` dyne/cm
Answer» Correct Answer - 1 `F=(2T)/(h)A=(2T)/(h)xx(m)/(rhoh)` or `F=(2Tm)/(rhoh^(2))`

Discussion

316.	A drop of Volume `V` is pressed between the two glass plates so as to spread to an area of `A`. If `T` is the surface tension, the normal force required to separate the glass plates isA. `sqrt((sigma)/(g(2rho-d)))`B. `sqrt((2sigma)/(g(2rho-d)))`C. `sqrt((6sigma)/(g(2rho-d)))`D. `sqrt((12sigma)/(g(2rho-d)))`
Answer» Correct Answer - D `2pirsigma+(1)/(2)xx(4)/(3)pir^(3)dg=(4)/(3)pir^(3)rhog` or `2pirsigma=(pir^(2)g)/(3)[4rho-2d]` or `r^(2)=(3xx2pisigma)/(g(2rho-2d))` or `r^(2)=(3sigma)/(g(2rho-d))` or `r=sqrt((3sigma)/(g(2rho-d)))` Diamter `=2r=sqrt((12sigma)/(g(2rho-d)))`

Discussion

317.	A drop of liquid pressed between two glass plates spreads to a circle of diameter 10 cm. Thickness of the liquid film is 0.5 mm and surface tension is `70xx10^(-3)Nm^(-1)` the force required to pull them apart isA. 4.4NB. 1.1NC. 2.2ND. 3.6N
Answer» Correct Answer - 3 `F=(2TA)/(d)`

Discussion

318.	Two syringes of different cross-sections (without needles) filled with water are connected with a tightly fitted rubber tube filled with water. Diameters of the smaller piston and larger piston are 1.0cm and 3.0 cm respectively. (a) Find the force on the larger piston when a force of 10N is applied to the smaller piston. (b) The smaller piston is paused in through 6.0 cm, much does the larger piston move out?
Answer» (a). Since pressure is transmitted undiminished throughout the fluid, `F_(2)=(A_(2))/(A_(1))F_(1)=(pi(3//2xx10^(-2)m)^(2))/(pi(1//2xx10^(-2)m)^(2))xx10N` `=90N` (b). Water is considered to be perfectly incompressible. Volume covered by the movement of smaller piston inwards is equal to volume moved outwards due to the larger piston `L_(1)A_(1)=L_(2)A_(2)` `L_(2)=(A_(1))/(A_(2))L_(1)=(pi(1//2xx10^(-2)m)^(2))/(pi(3//2xx10^(-2)m)^(2))xx6xx10^(-2)m` `cong0.67xx10^(-2)m=0.67cm` Note, atmospheric pressure is common to both pistons and has been ignored.

Discussion

319.	In the figure, an ideal liquid flows through the tube, which is of uniform cross section. The liquid has velocities `v_(A)` and `v_(B)`, and pressures `P_(A)` and `P_(B)` at the points `A` and `B`, respectively. Then A. `v_(B) gt v_(A)`B. `v_(B) =v_(A)`C. `P_(B) lt P_(A)`D. `P_(B)= P_(A)`
Answer» Correct Answer - B For a streamline flow of an ideal liquid, `v_(A)=v_(B)` . The pressure at B=Pressure at A+pressure dre to column of liquid of height AB.

Discussion

320.	A cube of ice of side length 10 cm is floating in water of density 1000 `kg//m^(3)`. Then pick up the correct statement (density of ice = 900 `kg//m^(3)`)A. 1 cm of the cube will be out of waterB. 9 cm of the cube will be out of waterC. 9 cm of the cube will be in waterD. 1 cm of the cube will be in water
Answer» Correct Answer - A::C

Discussion

321.	Pick out the wrong statement from the followingA. viscosity depends upon the nature of the liquidsB. generally viscosity of liquids is more than that of gasesC. in case of gases, viscosity decreases with increase in temperatureD. in case of liquids viscosity decreases with increase in temperature
Answer» Correct Answer - C Visosity involves transport of momentum had not of mass.

Discussion

322.	Consider a disk of mass `m`, radius `R` lying on a liquid layer of thickness T and coefficient of viscosity `eta` as shown in the fig. The coefficient of viscosity varies as `eta=eta_(0)x` (x measured from centre of the disk) at the given instant the disk is floating towards right with a velocity `v` as shown, find the force required to move the disk slowly at the given instant.A. `(2eta_(0)R^(2)v)/(T)`B. `(8eta_(0)R^(2)v)/(T)`C. `(pieta_(0)R^(2)v)/(T)`D. `(16eta_(0)R^(3)v)/(T)`
Answer» Correct Answer - C `df=etaA(dv)/(dx)` `f=int_(0)^(R)(eta_(0)x).(2pixdx)(V)/(T)` `f=(2)/(3).(pieta_(0)R^(3)V)/(T)`

Discussion

323.	In the arrangement shown two liquids of density `rho` and `2rho` are filled in a container the height of both liquids is h. there are two holes A and B at heights `h_(1)` and `h_(2)` from top liquid surface and bottom of the vessel. if `V_(1)` and `V_(2)` are the velocities of efflux at the two holes A and B respectively, find the correct graph. Take `=alpha((V_(2))/(V_(1)))^(2)`A. B. C. D.
Answer» Correct Answer - B `V_(1)^(2)=2gh_(1)` ….(1)k `rhogh+(2rho)g(h-h_(2))=(1)/(2)(2rho)V_(2)^(2)` `V_(2)^(2)=g(3h-2h_(2))` .(2) `((V_(2))/(V_(1)))^(2)=((3h)/(2h_(1))-(h_(2))/(h_(1)))` As `h_(2)` increases `((V_(2))/(V_(1)))^(2)` will decrease.

Discussion

324.	There is a howizontal film of soap solution. On it a thread is placed in the form of a loop. The film is pierced inside the loop and the thread becomes a circular loop of radius `R`. If the surface tension of the loop be `T`, then what will be the tension in the thread?A. `(pi R^(2))/(T)`B. `pi R^(2) T`C. `2 pi RT`D. 2 RT
Answer» Correct Answer - D

Discussion

325.	The cross-sectionss of a pipe at two points A and B are in the ratio 1.4. If the speed of water flowing through the pipe at point A is v, its speed at point B isA. 4vB. `(v)/(4)`C. 2vD. `(v)/(2)`
Answer» Correct Answer - B

Discussion

326.	Pressure is a scalar quantity, becauseA. it is the ratio of force of area and both force and area are vectorsB. it is the ratio of the magnitude of the force to areaC. it is the ratio of the componenet of the force normal to the areaD. it does not depend on the size of the area chosen
Answer» Correct Answer - B::C Pressure is defined as the ratio of magnitude of component of the force normal to the area and the area under consideration. As magnitude of component is considered , hence, it will not have any direction . So, pressure is a scalar quantity.

Discussion

327.	The quantity on which the rise of liquid in a capillary tube does not depend isA. density of liquidB. radius of capillary tubeC. angle of contactD. atmospheric pressure
Answer» Correct Answer - D

Discussion

328.	If the speed of a liquid flowing horizontally increases at a place, then the quantity that decreases there isA. Kinetic energyB. Potential energyC. PressureD. Density
Answer» Correct Answer - C

Discussion

329.	The fundametal quantity which has the same power in the dimensional formula of surface tension and coefficient of viscosity isA. massB. lengthC. timeD. none
Answer» Correct Answer - A

Discussion

330.	In a wind tunnel experiment the pressure on the upper and lower surfaces of the wings are 0.90`xx 10^(5)` Pa and 0.91 `xx10^(5)`Pa respectively .If the area of the wings is `40 m^(2)` the net liftng forcw on the wing isA. `2xx 10^(4)`NB. `4xx 10^(4)`NC. `6 xx 10^(4)`ND. `8 xx 10^(4)`N
Answer» Correct Answer - B Pressure differnce which provides the lift =Pressure difference `xx` Area of the wing `=(P_(2)xxP_(1))xxA=(0.91xx10^(5)-0.90xx10^(5))Paxx40 m^(2)` `=0.01xx10^(5) Pa xx 40 m^(2)=4xx10^(4) N`

Discussion

331.	Pressure is a scalar quantity, becauseA. it is the ratio of force to area and both force and area are vectors.B. it is the ratio of the magnitude of the force to areaC. it is the ratuo of the component of the force normal to the areaD. it depends on the size of the area chosen.
Answer» Correct Answer - C Pressure is a scaler quantity because it is the ratio of the component of the force normal to the area and it is independent on the size of the area chosen.

Discussion

332.	A beaker is partly filled with water, the beaker and the contents have a mass of 50 gm. A piece of wood having a volume of 5 cc. is floated in the beaker. The density of wood is `0.8(g)/(c.c)` the mass of the beaker and its contents:A. 50 gB. 54 gC. 46 gD. 56.25 g
Answer» Correct Answer - 2 Weight of beaker `=` weight of water (with beaker `+` upthrust on wood

Discussion

333.	A force of 10 N is requrid to draw rectangular glass plate on the surface of a liquid with some velocity. Force needed to draw another glass plate of 3 times length and 2 times width isA. `(5)/(3)N`B. `10N`C. `60N`D. `30N`
Answer» Correct Answer - C `F=etaA(dv)/(dx),FalphaA`

Discussion

334.	The velocity of water in river is 180 km `h^(-1)` near the surface .If the river is 5 m deep,then the shearing stress between the surface layer and the bottom layer is ( cofficient of viscosity of water `eta =10^(-3)` Pa s)A. `10^(-2)N m^(-2)`B. `10^(-3)N m^(-2)`C. `10^(-4)N m^(-2)`D. `10^(-5)N m^(-2)`
Answer» Correct Answer - B As the velocity of water at the bottom of the river is zero, `dv=18 km h^(-1)=18xx(5)/(18)=5 m s^(-1)` Also , `dx=5 m, eta=10^(-3)` Pa s Force of viscosity , `F=etaA(dv)/(dx)` `therefore` Shearing stress, `=(F)/(A)=eta(dv)/(dx)` `=(10^(-3)xx5)/(5)=10^(-3) N m^(-2)`

Discussion

335.	If the shearing stress between the horizontal layers of water in a river is 1.5 milli `"newton"//m^(2)` and `eta_("water")=1xx10^(-3)Pa.s` The velocity gradient is …`s^(-1)`A. 1.5B. 3C. 0.7D. 1
Answer» Correct Answer - A `(dv)/(dx)=(F)/(Aeta)`

Discussion

336.	The velocity of water in a river is 18 kmph near the surface. If the river is 4 m deep, the shearing stress between horizontal layers of water in `Nm^(-2)` is `(eta_("water")=1xx10^(-3)pa.s)`A. `2.5xx10^(-3)`B. `1.25xx10^(-3)`C. `0.75xx10^(-3)`D. 0
Answer» Correct Answer - 2 `(F)/(A)=eta(dv)/(dx)`

Discussion

337.	If the atmospheric pressure is 76 cm of Hg at what depth of water the pressure will becomes 2 atmospheres nearly.A. 862 cmB. 932 cmC. 982 cmD. 1033 cm
Answer» Correct Answer - 4 `P-P_(0)=hrhog`

Discussion

338.	Find the pressure exerted below a column of water, open to the atmosphere, at depth (i) 5 m (ii) 20 m (Given, density of water = `1 xx 10^(3)"kg m"^(-3), g = 10 m s^(-2)`)
Answer» (i) Pressure at a depth of 5 m `P = P_(a) + rho gh` `= 1.013 xx 10^(5) Pa + (1 xx 10^(3) kg m^(-3))(10 ms^(-2))(5m)` `=1.013 xx 10^(5) Pa + 0.5 xx 10^(5) Pa` `= 1.513 xx 10^(5) Pa` (ii) Pressure at a depth of 20 m `P = P_(a) + rho gh` `= 1.013 xx 10^(5) Pa + (1 xx 10^(3) kg m^(-3))(10 ms^(-2))(20 m)` `= 1.013 xx 10^(5) Pa + 2 xx 10^(5) Pa` `= 3.013 xx 10^(5) Pa` = 3 atm

Discussion

339.	A manometer tube contains mercury of density `13.6 xx 10^(3)` kg `m^(-3)`. What difference in the levels of mercury in the two arms is indicated by a gauge pressure of `1.03 xx 10^(5) Pa`?
Answer» Correct Answer - 77 cm

Discussion

340.	A vertical off-shore structure is built to withstand a a maximum stress of `10^(9)Pa`. Is the structure suitabel for putting upon top of an oil well in bombay high? Take the depth of the sea to be roughly 3 km, and ignore oceam currents.
Answer» Here, maximum stress `=10^(9)Pa,h=3km=3xx10^(3)m` `p("water")=10^(3)kg//m^(3) and g=9.8m//s^(2)` The structure will be suitable for putting upon top of an oil well provided the pressure exerted by sea water is less than the maximum stress it can bear. Pressure due to sea water `P=h rho g=3xx10^(3)xx10^(3)xx9.8Pa=2.94xx10^(7)Pa` Since the pressure of sea water is less than the maximum

Discussion

341.	A 50 kg. girl wearing high heel shoes balance on a single heel. The heel is circular with a diameter 1 cm. what is the pressure exerted by the heel on the horizontal floor?
Answer» Mass of girl `m=50kg` `therefore` force on the heel, `F=mg=50xx9.8=490N` Diameter, `D=1.0cm=1xx10^(-2)m` `therefore` Area, `A=(piD^(2))/(4)=(3.14xx(1xx10^(-2))^(2))/(4)=7.85xx10^(-5)m^(2)` `therefore` Pressure, `P=(F)/(A)=(490)/(7.85xx10^(-5))=6.24xx10^6Pa`.

Discussion

342.	Along a streamline,A. the velocity of a fluid particle remains constantB. the velocity of all fluid particles crossing a given position is constantC. the velocity of all fluid particles at a given instant is constantD. the speed of a fluid particle remains constant
Answer» Correct Answer - B As we know for a streamline flow of a liquid velocity of each particle at a particular cross-section is constant, because Av-constant (law of continuity between two cross-section of a tube of flow.

Discussion

343.	Streamline flow is more likely for liquid withA. high denistyB. high viscosityC. low densityD. low viscosity
Answer» Correct Answer - B::C Streamline flow is mmore likely for liquids having low density. We know that greater the coefficient of viscosity of a liquid more will be veloctiy gradient hence each line of flow can be easily defferentiated. Also higher the coefficient of viscosity lower will be Reynolds number, hence flow more like to be streamline.

Discussion

344.	Three capillaries of length `L, (L)/(2) and (L)/(3)` are connected in a series. Their radii are `r, (r)/(2) and (r)/(3)` respectively. If a streamlined flow is to be maintained and pressure difference across the first capillary is `rho`, then the pressure difference across the second capillary will beA. `2 rho`B. `8 rho`C. `rho`D. `(rho)/(2)`
Answer» Correct Answer - B

Discussion

345.	Which of the following diagrams does not represent a streamline flow?A. B. C. D.
Answer» Correct Answer - D In a streamline flow at any given point, the velocity of each passing fluid particles remains constant. If we consider a cross-sectional area, then a point on the area cannot have different velocities at the same time, hence two streamlines of flow cannot cross each other.

Discussion

346.	Along a streamline,A. the velocity of a fluid particle remains constantB. the velocity of all fluid particles crossing a given position is constantC. the velocity of all fluid particles at a given instant is constantD. the speed of a fluid particle remains constant.
Answer» Correct Answer - B `A_(1)v_(1)=A_(2)v_(2)`

Discussion

347.	A glass capillary tube is of the shape of a truncated cone with an apex angle `alpha` so that its two ends have cross sections of different radii. When dipped in water vertically, water rises in it to a high h, where the radius of its cross section is b. If the surface tension of water is S, its density if `rho`, and its contact angle with glass is `theta`, the value of h will be (g is the acceleration due to gravity) A. `(2S)/(brhog)cos(theta-alpha)`B. `(2S)/(brhog)cos(theta+alpha)`C. `(2S)/(brhog)cos(theta-(alpha)/(2))`D. `(2S)/(brhog)cos(theta+(alpha)/(2))`
Answer» Correct Answer - D `(b)/(R)=cos(theta+(alpha)/(2))` Using pressure equation along the path MNTK `p_(0)-(2S)/(R)+hrhog=p_(0)`

Discussion

348.	Statement-1: A light celluloid ball placed in a stream of gas or water issuing at a high velocity from a tube with a narrow neck, the ball floats freely however in this stream (fig) Statement-2: The gas is the stream has a high velocity, the pressure inside the stream is above atmospheric.A. Statement-I is true, statement-2 true and statements-2 is a correct explanation for statements-1B. Statement 1 is true, statement 2 is true, statement-2 is not a correct explanation for statement 1C. Statement 1 is true, statement 2 is falseD. Statement 1 is false, statement 2 is true
Answer» Correct Answer - C Bernoullis principle.

Discussion

349.	A spray gun is shown in the figure where a piston pushes air out of a nozzle. A thin tube of uniform cross section is connected to the nozzle. The other end of the tube is in a small liquid container. As the piston pushes air through the nozzle, the liquid from the container rises into the nozzle and is sprayed out. For the spray gun shown, the radii of the piston and the nozzle are 20mm and 1mm respectively. The upper end of the container is open to the atmosphere. If the piston is pushed at a speed of `5mms^-1`, the air comes out of the nozzle with a speed ofA. `0.1ms^(-1)`B. `1ms^(-1)`C. `2ms^(-1)`D. `8ms^(-1)`
Answer» Correct Answer - C From `A_(1)v_(1)=A_(2)v_(2)` `v_(2)=2m//s`

Discussion

350.	A spray gun is shown in the figure where a piston pushes air out of a nozzle. A thin tube of uniform cross section is connected to the nozzle. The other end of the tube is in a small liquid container. As the piston pushes air through the nozzle, the liquid from the container rises into the nozzle and is sprayed out. For the spray gun shown, the radii of the piston and the nozzle are 20mm and 1mm respectively. The upper end of the container is open to the atmosphere. If the density of air is `rho_a`, and that of the liquid `rho_l`, then for a given piston speed the rate (volume per unit time) at which the liquid is sprayed will be proportional toA. `sqrt((rho_(a))/(rho_(l)))`B. `sqrt(rho_(a)rho_(l))`C. `sqrt((rho_(l))/(rho_(a)))`D. `rho_(l)`
Answer» Correct Answer - A `p_(1)=p_(2)=(1)/(2)rho_(a)v_(a)^(2)` `p_(3)-p_(2)=(1)/(2)rho_(1)v_(l)^(2)` `p_(3)=p_(1)` `:. (1)/(2)rho_(1)v_(l)^(2)` `impliesv_(l)=sqrt((rho_(a))/(rho_(l)))v_(a)` `:.` Volume flow rate `propsqrt((rho_(a))/(rho_(l)))`

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