Mechanical Properties of Fluids

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

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

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 liquid column of height 0.04 cm balances excess pressure of a soap bubble of certain radius. If density of liquid is 8 103 kg m-3 and surface tension of soap solution is 0.28 N m-1, then diameter of the soap bubble is cm. (if g = 10 m s-2)

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

Small water droplets of radius 0.01 mm are formed in the upper atmosphere and falling with a terminal velocity of 10 cm/s. Due to condensation, if 8 such droplets are coalesced and formed a larger drop, the new terminal velocity will be cm/s.

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 )

A big drop is formed by coalescing 1000 small droplets of water. The ratio of surface energy of 1000 droplets to that of energy of big drop is 10x. The value of x is .

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

[figure] A hydraulic press containing water has two arms with diameters as mentioned in the figure. A force of 10 N is applied on the surface of water in the thinner arm. The force required to be applied on the surface of water in the thicker arm to maintain equilibrium of water is N.

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.

A soap bubble is blown to a diameter of 7 cm. 36960 erg of work is done in blowing it further. If surface tension of soap solution is 40 dyne/cm then the new radius is cm. Take ( = 227 ).

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.

Mercury is filled in a tube of radius 2 cm up to a height of 30 cm. The force exerted by mercury on the bottom of the tube is N. (Given, atmospheric pressure = 105 N m-2, density of mercury = 1.36 104 kg m-3, g = 10 m s-2, = 227)

A plane is in level flight at constant speed and each of its two wings has an area of 40 m2. If the speed of the air is 180 km/h over the lower wing surface and 252 km/h over the upper wing surface, the mass of the plane is kg. (Take air density to be 1 kg m-3 and g = 10 m s-2)

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

A big drop is formed by coalescing 1000 small identical drops of water. If E1 be the total surface energy of 1000 small drops of water and E2 be the surface energy of single big drop of water, then E1:E2 is x:1 where x= .