Mechanical Properties of Fluids

A spherical ball of radius 1 10-4 m and density 105 kg/m3 falls freely under gravity through a distance h before entering a tank of water. If after entering in water the velocity of the ball does not change, then the value of h is approximately: (The coefficient of viscosity of water is 9.8 10-6 N s/m2)

1. 2518 m
2. 2396 m
3. 2249 m
4. 2296 m

Correct Bernoulli's equation is (symbols have their usual meaning) :

1. P + 12 gh + 12 v2 = constant
2. P + mgh + 12mv2 = constant
3. P + gh + v2 = constant
4. P + gh + 12 v2 = constant

A cube of ice floats partly in water and partly in kerosene oil. The ratio of volume of ice immersed in water to that in kerosene oil (specific gravity of Kerosene oil = 0.8, specific gravity of ice = 0.9): [figure]

1. 5 : 4
2. 9 : 10
3. 8 : 9
4. 1 : 1

A small ball of mass m and density is dropped in a viscous liquid of density 0. After sometime, the ball falls with constant velocity. The viscous force on the ball is :

1. mg (1 - 0 )
2. mg ( 0 - 1 )
3. mg (1 - 0 )
4. mg (1 + 0 )

Pressure inside a soap bubble is greater than the pressure outside by an amount : (given : R = Radius of bubble, S = Surface tension of bubble)

1. SR
2. 4SR
3. 4RS
4. 2SR

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

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

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

1. Statement I is correct but Statement II is incorrect.
2. Both Statement I and Statement II are correct.
3. Both Statement I and Statement II are incorrect.
4. Statement I is incorrect but Statement II is correct.

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.

A big drop is formed by coalescing 1000 small droplets of water. The surface energy will become :

1. 1100 th
2. 110 th
3. 100 times
4. 10 times

A small steel ball is dropped into a long cylinder containing glycerine. Which one of the following is the correct representation of the velocity time graph for the transit of the ball?

1. [figure]
2. [figure]
3. [figure]
4. [figure]

A small spherical ball of radius r, falling through a viscous medium of negligible density has terminal velocity 'v'. Another ball of the same mass but of radius 2r, falling through the same viscous medium will have terminal velocity:

1. 4v
2. 2v
3. v4
4. v2

Given below are two statements: In the light of the above statements, choose the most appropriate 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 true but Statement II is false
4. Statement I is false but Statement II is true

A small liquid drop of radius R is divided into 27 identical liquid drops. If the surface tension is T, then the work done in the process will be:

1. 4 R2T
2. 8 R2T
3. 18 R2T
4. 3 R2T

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

1. Statement I is correct but statement II is incorrect
2. Statement I is incorrect but Statement II is correct
3. Both Statement I and Statement II are incorrect
4. Both Statement I and Statement II are correct