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

The surface tension of a soap solution is 3.5 10-2 N/m. The work required to increase the radius of a soap bubble from 1 cm to 2 cm is 10-6 J. The value of is . ( =22/7)

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

A tub is filled with water and a wooden cube 10 cm 10 cm 10 cm is placed in the water. The wooden cube is found to float on the water with a part of it submerged in water. When a metal coin is placed on the wooden cube, the submerged part is increased by 3.87 cm. The mass of the metal coin is gram. (Take water density as 1 g/cm3 and density of wood as 0.4 g/cm3)

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

Sixty four raindrops of radius 1 mm each falling down with a terminal velocity of 10 cm/s coalesce to form a bigger drop. The terminal velocity of bigger drop is cm/s.

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 soap bubble of surface tension 0.04 N/m is blown to a diameter of 7 cm. If (15000 - x) of work is done in blowing it further to make its diameter 14 cm, then the value of x is . ( = 22/7)

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

The terminal velocity of a metallic ball of radius 6 mm in a viscous fluid is 20 cm/s. The terminal velocity of another ball of same material and having radius 3 mm in the same fluid will be cm/s.

A cube having a side of 10 cm with unknown mass and 200 gm mass were hung at two ends of a uniform rigid rod of 27 cm long. The rod along with masses was placed on a wedge keeping the distance between wedge point and 200 gm weight as 25 cm. Initially the masses were not at balance. A beaker is placed beneath the unknown mass and water is added slowly to it. At given point the masses were in balance and half volume of the unknown mass was inside the water. (Take the density of unknown mass is more than that of the water, the mass did not absorb water and water density is 1 gm/cm3.) The unknown mass is kg.

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

The excess pressure inside a soap bubble A in air is half the excess pressure inside another soap bubble B in air. If the volume of the bubble A is n times the volume of the bubble B, then, the value of n is .

A vessel with square cross-section and height of 6 m is vertically partitioned. A small window of 100 cm2 with hinged door is fitted at a depth of 3 m in the partition wall. One part of the vessel is filled completely with water and the other side is filled with the liquid having density 1.5 103 kg/m3. What force one needs to apply on the hinged door so that it does not get opened? (Acceleration due to gravity = 10 m/s2)

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]

In a hydraulic lift, the surface area of the input piston is 6 cm2 and that of the output piston is 1500 cm2. If 100 N force is applied to the input piston to raise the output piston by 20 cm, then the work done is kJ.

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