Mechanical Properties of Fluids · Question 14

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