Mechanical Properties of Fluids

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

An air bubble of radius 1.0 mm is observed at a depth 20 cm below the free surface of a liquid having surface tension 0.095 J/m2 and density 103 kg/m3. The difference between pressure inside the bubble and atmospheric pressure is N/m2. (Take g=10 m/s2)

Two soap bubbles of radius 2 cm and 4 cm , respectively, are in contact with each other. The radius of curvature of the common surface, in cm , is .

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