Mechanical Properties of Fluids

A small sphere of radius 'r' falls from rest in a viscous liquid. As a result, heat is produced due to viscous force. The rate of production of heat when the sphere attains its terminal velocity, is proportional to

1. r3
2. r2
3. r5
4. r4

A U tube with both ends open to the atmosphere, is partially filled with water. Oil, which is immiscible with water, is poured into one side until it stands at a distance of 10 mm above the water level on the other side. Meanwhile the water rises by 65 mm from its original level (see diagram). The density of the oil is [figure]

1. 425 kg m-3
2. 800 kg m-3
3. 928 kg m-3
4. 650 kg m-3

Two non-mixing liquids of densities and n (n > 1) are put in a container. The height of each liquid is h. A solid cylinder of length L and density d is put in this container. The cylinder floats with its axis vertical and length pL (p < 1) in the denser liquid. The density d is equal to

1. \2 + (n - 1)p\
2. \1 + (n - 1)p\
3. \1 + (n + 1)p\
4. \2 + (n + 1)p\

A rectangular film of liquid is extended from (4 cm 2 cm) to (5 cm 4 cm). If the work done is 3 10-4 J, the value of the surface tension of the liquid is

1. 0.250 N m-1
2. 0.125 N m-1
3. 0.2 N m-1
4. 8.0 N m-1

Three liquids of densities 1, 2 and 3 (with 1 > 2 > 3), having the same value of surface tension T, rise to the same height in three identical capillaries. The angles of contact 1, 2 and 3 obey

1. 2 > 1 > 2 > 3 0
2. 0 1 < 2 < 3 < 2
3. 2 < 1 < 2 < 3 <
4. > 1 > 2 > 3 > 2

The heart of a man pumps 5 litres of blood through the arteries per minute at a pressure of 150 mm of mercury. If the density of mercury be 13.6 103 kg/m3 and g = 10 m/s2 then the power (in watt) is

1. 3.0
2. 1.50
3. 1.70
4. 2.35

The cylindrical tube of a spray pump has radius R, one end of which has n fine holes, each of radius r. If the speed of the liquid in the tube is V, the speed of the ejection of the liquid through the holes is

1. VR2n3r2
2. V2Rnr
3. VR2n2r2
4. VR2nr2

Water rises to a height h in capillary tube. If the length of capillary tube above the surface of water is made less than h, then

1. water rises upto a point a little below the top and stays there.
2. water does not rise at all.
3. water rises upto the tip of capillary tube and then starts overflowing like a fountain.
4. water rises upto the top of capillary tube and stays there without overflowing.

A wind with speed 40 m/s blows parallel to the roof of a house. The area of the roof is 250 m2. Assuming that the pressure inside the house is atmospheric pressure, the force exerted by the wind on the roof and the direction of the force will be ( air = 1.2 kg/m3)

1. 2.4 105 N, upwards
2. 2.4 105 N, downwards
3. 4.8 105 N, downwards
4. 4.8 105 N, upwards

A certain number of spherical drops of a liquid of radius r coalesce to form a single drop of radius R and volume V. If T is the surface tension of the liquid, then

1. energy = 4VT ( 1r - 1R ) is released.
2. energy = 3VT ( 1r + 1R ) is absorbed.
3. energy = 3VT ( 1r - 1R ) is released.
4. energy is neither released nor absorbed.