Mechanical Properties of Fluids

A liquid of density 600 kg/m3 flowing steadily in a tube of varying cross-section. The cross-section at a point A is 1.0 cm2 and that at B is 20 mm2. Both the points A and B are in same horizontal plane, the speed of the liquid at A is 10 cm/s. The difference in pressures at A and B points is Pa.

1. 18
2. 144
3. 36
4. 72

A spherical liquid drop of radius R acquires the terminal velocity v1 when falls through a gas of viscosity . Now the drop is broken into 64 identical droplets and each droplet acquires terminal velocity v2 falling through the same gas. The ratio of terminal velocities v1/v2 is .

1. 4
2. 0.25
3. 32
4. 16

A cylindrical vessel of 40 cm radius is completely filled with water and its capacity is 528 dm3 (dm : decimeter). The vessel is placed on a solid block of exactly same height as vessel. If a small hole is made at 70 cm below the top of water level, then horizontal range of water falling on the ground in the beginning is cm.

1. 120 2
2. 140 2
3. 140 3
4. 120 3

Eight mercury drops, each of radius r, coalesce to form a bigger drop. The surface energy released in this process is . (S is the surface tension of mercury).

1. 8 r2S
2. 16 r2S
3. 64 r2S
4. 4 r2S

A water spray gun is attached to a hose of cross sectional area 30 cm2. The gun comprises of 10 perforations each of cross sectional area of 15 mm2. If the water flows in the hose with the speed of 50 cm/s, calculate the speed at which the water flows out from each perforation. (Neglect any edge effects)

1. 100 m/s
2. 10 m/s
3. 1000 m/s
4. 15 102 m/s

A liquid drop of diameter 2 mm breaks into 512 droplets. The change in surface energy is 10-6 J. The value of is . (Take surface tension of liquid = 0.08 N/m)

1. 10
2. 7
3. 8
4. 11

The surface tension of a soap bubble is 0.03 N/m. The work done in increasing the diameter of bubble from 2 cm to 6 cm is 10-4 J. The value of is . (Take =3.14)

1. 0.86
2. 0.64
3. 1.92
4. 7.68

If an air bubble of diameter 2 mm rises steadily through a liquid of density 2000 kg/m3 at a rate of 0.5 cm/s, then the coefficient of viscosity of liquid is Poise. (Take g=10 m/s2)

1. 0.88
2. 8.8
3. 88.8
4. 0.088

A cubical block of density b = 600 kg/m3 floats in a liquid of density l = 900 kg/m3. If the height of block is H = 8.0 cm, then height of the submerged part is cm.

1. 6.3
2. 4.3
3. 7.3
4. 5.3

A small metallic sphere of diameter 2 mm and density 10.5 g/cm3 is dropped in glycerine having viscosity 10 Poise and density 1.5 g/cm3 respectively. The terminal velocity attained by the sphere is cm/s. ( = 227 and g = 10 m/s2)

1. 1.0
2. 1.5
3. 3.0
4. 2.0

A cylindrical tube AB of length l, closed at both ends contains an ideal gas of 1 mol having molecular weight M. The tube is rotated in a horizontal plane with constant angular velocity about an axis perpendicular to AB and passing through the edge at end A, as shown in the figure. If PA and PB are the pressures at A and B respectively, then (Consider the temperature is same at all points in the tube) [figure]

1. PB = PA e ( M 2 l23RT )
2. PB = PA
3. PB = PA e ( M 2 l22RT )
4. PB = PA e ( M 2 l2RT )

Given below are two statements : In the light of the above statements, choose the correct answer from the options given below

1. Statement I is false but Statement II is true
2. Statement I is true but Statement II is false
3. Both Statement I and Statement II are false
4. Both Statement I and Statement II are true

When a part of a straight capillary tube is placed vertically in a liquid, the liquid rises up to certain height h. If the inner radius of the capillary tube, density of the liquid and surface tension of the liquid decrease by 1% each, then the height of the liquid in the tube will change by %.

1. +3
2. +1
3. -1
4. -3

Water flows through a horizontal tube as shown in the figure. The difference in height between the water columns in vertical tubes is 5 cm and the area of cross-sections at A and B are 6 cm2 and 3 cm2 respectively. The rate of flow will be cm3/s. (take g = 10 m/s2) [figure]

1. 100 3
2. 200 3
3. 200 6
4. 200 3

Surface tension of two liquids (having same densities), T1 and T2, are measured using capillary rise method utilizing two tubes with inner radii of r1 and r2 where r1 > r2. The measured liquid heights in these tubes are h1 and h2 respectively. [Ignore the weight of the liquid above the lowest point of meniscus]. The heights h1 and h2 and surface tensions T1 and T2 satisfy the relation :

1. h1 > h2 and T1 = T2
2. h1 < h2 and T1 = T2
3. h1 > h2 and T1 < T2
4. h1 = h2 and T1 = T2

A capillary tube of radius 0.1 mm is partly dipped in water (surface tension 70 dyn/cm and glass water contact angle 0 ) with 30 inclined with the vertical. The length of water risen in the capillary is cm. (Take g = 9.8 m/s2)

1. 825
2. 685
3. 572
4. 715

Two liquids A and B have A and B as contact angles in a capillary tube. If K = A / B, then identify the correct statement:

1. K is negative, then liquid A and liquid B have convex meniscus.
2. K is negative, then liquid A and liquid B have concave meniscus.
3. K is zero, then liquid A has convex meniscus and liquid B has concave meniscus.
4. K is negative, then liquid A has concave meniscus and liquid B has convex meniscus.

Consider a completely full cylindrical water tank of height 1.6 m and of cross-sectional area 0.5 m2. It has a small hole in its side at a height 90 cm from the bottom. Assume, the cross-sectional area of the hole to be negligibly small as compared to that of the water tank. If a load 50 kg is applied at the top surface of the water in the tank then the velocity of the water coming out at the instant when the hole is opened is: (g = 10 m/s2)

1. 2 m/s
2. 5 m/s
3. 3 m/s
4. 4 m/s

A solid steel ball of diameter 3.6 mm acquired terminal velocity 2.45 10-2 m/s while falling under gravity through an oil of density 925 kg m-3. Take density of steel as 7825 kg m-3 and g as 9.8 m/s2. The viscosity of the oil in SI unit is

1. 2.18
2. 1.68
3. 2.38
4. 1.99

Two water drops each of radius 'r' coalesce to form a bigger drop. If 'T' is the surface tension, the surface energy released in this process is :

1. 4 r2 T [2 - 21/3 ]
2. 4 r2 T[1 + 2]
3. 4 r2 T [2 - 22/3 ]
4. 4 r2 T[ 2 - 1]

Consider following statements: Choose the correct answer from the options given below:

1. B, C, D Only
2. C, D, E Only
3. A, D, E Only
4. A, B, C Only

A 400 g solid cube having an edge of length 10 cm floats in water. How much volume of the cube is outside the water? (Given: density of water = 1000 kg m-3)

1. 400 cm3
2. 600 cm3
3. 1400 cm3
4. 4000 cm3

An air bubble of radius 0.1 cm lies at a depth of 20 cm below the free surface of a liquid of density 1000 kg/m3. If the pressure inside the bubble is 2100 N/m2 greater than the atmospheric pressure, then the surface tension of the liquid in SI unit is (use g=10 m/s2)

1. 0.02
2. 0.05
3. 0.25
4. 0.1

The amount of work done to break a big water drop of radius 'R' into 27 small drops of equal radius is 10 J. The work done required to break the same big drop into 64 small drops of equal radius will be

1. 20 J
2. 10 J
3. 5 J
4. 15 J

Given below are two statements: In the light of the above statements, choose the correct answer from the options given below

1. Both Statement I and Statement II are false
2. Both Statement I and Statement II are true
3. Statement I is false but Statement II is true
4. Statement I is true but Statement II is false

Water flows in a horizontal pipe whose one end is closed with a valve. The reading of the pressure gauge attached to the pipe is P1. The reading of the pressure gauge falls to P2 when the valve is opened. The speed of water flowing in the pipe is proportional to

1. (P1-P2)2
2. P1-P2
3. P1-P2
4. (P1-P2)4

A tube of length L is shown in the figure. The radius of cross section at the point (1) is 2 cm and at the point (2) is 1 cm , respectively. If the velocity of water entering at point (1) is 2 m/s, then velocity of water leaving the point (2) will be [figure]

1. 4 m/s
2. 6 m/s
3. 2 m/s
4. 8 m/s

A small rigid spherical ball of mass M is dropped in a long vertical tube containing glycerine. The velocity of the ball becomes constant after some time. If the density of glycerine is half of the density of the ball, then the viscous force acting on the ball will be (consider g as acceleration due to gravity)

1. 2Mg
2. 32Mg
3. Mg2
4. Mg

A sphere of relative density and diameter D has concentric cavity of diameter d. The ratio of Dd, if it just floats on water in a tank is :

1. ( - 2 + 2 )1/3
2. ( + 1 - 1 )1/3
3. ( - 1 )1/3
4. ( - 1 )1/3

The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. The ratio between the volume of the first and the second bubble is:

1. 1 : 9
2. 1 : 27
3. 1 : 81
4. 1 : 3