Mechanical Properties of Fluids · Question 11

Two copper vessels A and B have the same base area but of different shapes. A takes twice the volume of water as that B requires to fill upto a particular common height. Then the correct statement among the following is :

1. Vessel B weighs twice that of A.
2. Pressure on the base area of vessels A and B is same.
3. Pressure on the base area of vessels A and B is not same.
4. Both vessels A and B weigh the same.

The terminal velocity of a copper ball of radius 5 mm falling through a tank of oil at room temperature is 10 cm s-1. If the viscosity of oil at room temperature is 0.9 kg m-1 s-1, the viscous drag force is :

1. 4.23 10-6 N
2. 8.48 10-3 N
3. 8.48 10-5 N
4. 4.23 10-3 N

The velocity of a small ball of mass M and density d, when dropped in a container filled with glycerin becomes constant after some time. If the density of glycerin is d2, then the viscous force acting on the ball will be :

1. 2Mg
2. Mg2
3. Mg
4. 32Mg

A capillary tube of radius r is immersed in water and water rises in it to a height h. The mass of the water in the capillary is 5 g. Another capillary tube of radius 2r is immersed in water. The mass of water that will rise in this tube is :

1. 5.0 g
2. 10.0 g
3. 20.0 g
4. 2.5 g

A small hole of area of cross-section 2 mm2 is present near the bottom of a fully filled open tank of height 2 m. Taking g = 10 m/s2, the rate of flow of water through the open hole would be nearly :

1. 8.9 10-6 m3/s
2. 2.23 10-6 m3/s
3. 6.4 10-6 m3/s
4. 12.6 10-6 m3/s

A soap bubble, having radius of 1 mm, is blown from a detergent solution having a surface tension of 2.5 10-2 N/m. The pressure inside the bubble equals the pressure at a point Z0 below the free surface of water in a container. Taking g = 10 m/s2, density of water = 103 kg/m3, the value of Z0 is :

1. 1 cm
2. 10 cm
3. 100 cm
4. 0.5 cm

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