A small spherical solid ball is dropped in a viscous liquid. Its journey in the liquid is best described in the figure by :
1. Curve A
2. Curve B
3. Curve C
4. Curve D
Water flows through a frictionless duct with a cross-section varying as shown in the figure. Pressure p at points along the axis is represented by
1. 2.
3. 4.
Equation of continuity based on :
1. Conservation of mass
2. Conservation of energy
3. Conservation of angular momentum
4. None of these
An incompressible liquid travels as shown in the figure. The speed of the fluid in the lower branch will :
1. 1 m/s
2. 1.5 m/s
3. 2.25 m/s
4. 3 m/s
The approximate depth of an ocean is 2700 m. The compressibility of water is 45.4 x 10-11 Pa-1 and density of water is 103kg/m3. What fractional compression of water will be obtained at the bottom of the ocean?
(1)0.8x10-2
(2)1.0x10-2
(3)1.2x10-2
(4)1.4x10-2
The heart of a man pumps 5 L of blood through the arteries per minute at a pressure of 150 mm of mercury. If the density of mercury is \(13.6\times 10^3\)kg/m3 and g =10 m/s2, then the power of heart in watt is:
1. 1.70
2. 2.35
3. 3.0
4. 1.50
Which two of the following five physical parameters have the same dimensions ?
(1) energy density
(2) refractive index
(3) dielectric constant
(4) Young's modulus
(5) magnetic field
1. 2 and 4
2. 3 and 5
3. 1 and 4
4. 1 and 5
An inverted bell lying at the bottom of a lake 47.6 m deep has 50 cm3 of air trapped in it. The bell is brought to the surface of the lake. The volume of the trapped air will be (atmospheric pressure = 70 cm of Hg and density of Hg = 13.6 g/cm3)
(1) 350 cm3
(2) 300 cm3
(3) 250 cm3
(4) 22 cm3
A siphon in use is demonstrated in the following figure. The density of the liquid flowing in siphon is 1.5 gm/cc. The pressure difference between the point P and S will be
(1)
(2)
(3) Zero
(4) Infinity
The height of a mercury barometer is 75 cm at sea level and 50 cm at the top of a hill. Ratio of density of mercury to that of air is . The height of the hill is
(1) 250 m
(2) 2.5 km
(3) 1.25 km
(4) 750 m
The value of g at a place decreases by 2%. The barometric height of mercury
(1) Increases by 2%
(2) Decreases by 2%
(3) Remains unchanged
(4) Sometimes increases and sometimes decreases
A barometer kept in a stationary elevator reads 76 cm. If the elevator starts accelerating up, the reading will be
(1) Zero
(2) Equal to 76 cm
(3) More than 76 cm
(4) Less than 76 cm
A closed rectangular tank is completely filled with water and is accelerated horizontally with an acceleration a towards right. Pressure is (i) maximum at, and (ii) minimum at
(1) (i) B (ii) D
(2) (i) C (ii) D
(3) (i) B (ii) C
(4) (i) B (ii) A
A beaker containing a liquid is kept inside a big closed jar. If the air inside the jar is continuously pumped out, the pressure in the liquid near the bottom of the beaker will
1. Increase
2. Decrease
3. Remain constant
4. First decrease and then increase
A given shaped glass tube having uniform cross section is filled with water and is mounted on a rotatable shaft as shown in figure. If the tube is rotated with a constant angular velocity then
(1) Water levels in both sections A and B go up
(2) Water level in Section A goes up and that in B comes down
(3) Water level in Section A comes down and that in B it goes up
(4) Water levels remains same in both sections
An incompressible liquid flows through a horizontal tube as shown in the following fig. Then the velocity v of the fluid is
(1) 3.0 m/s
(2) 1.5 m/s
(3) 1.0 m/s
(4) 2.25 m/s
Spherical balls of radius 'r' are falling in a viscous fluid of viscosity '' with a velocity 'v'. The retarding viscous force acting on the spherical ball is
(1) inversely proportional to 'r' but directly proportional to velocity 'v'.
(2) directly proportional to both radius 'r' and velocity 'v'.
(3) inversely proportional to both radius 'r' and velocity 'v'.
(4) directly proportional to 'r' but inversely proportional to 'v'.
A ball of radius r and density falls freely under gravity through a distance h before entering water. Velocity of ball does not change even on entering water. If viscosity of water is , the value of h is given by
(a)
(b)
(c)
(d)
A liquid flows in a tube from left to right as shown in figure. and are the cross-sections of the portions of the tube as shown. Then the ratio of speeds will be
(1)
(2)
(3)
(4)
The pans of a physical balance are in equilibrium. Air is blown under the right hand pan; then the right hand pan will
(1) Move up
(2) Move down
(3) Move erratically
(4) Remain at the same level
According to Bernoulli's equation
The terms A, B and C are generally called respectively:
1. Gravitational head, pressure head and velocity head
2. Gravity, gravitational head and velocity head
3. Pressure head, gravitational head and velocity head
4. Gravity, pressure and velocity head
A sniper fires a rifle bullet into a gasoline tank making a hole 53.0 m below the surface of gasoline. The tank was sealed at 3.10 atm. The stored gasoline has a density of 660 . The velocity with which gasoline begins to shoot out of the hole is
(a) 27.8 (b) 41.0
(c) 9.6 (d) 19.7
A tank is filled with water up to a height H. Water is allowed to come out of a hole P in one of the walls at a depth D below the surface of water. Express the horizontal distance x in terms of H and D
(a)
(b)
(c)
(d)
A large tank of cross-section area A is filled with water to a height H. A small hole of area 'a' is made at the base of the tank. It takes time to decrease the height of water to ; and it takes time to take out the rest of water. If , then the value of is
(a) 2 (b) 3
(c) 4 (d)
A small drop of water falls from rest through a large height h in air; the final velocity is
(1)
(2)
(3)
(4) Almost independent of h
Water is flowing in a pipe of diameter 4 cm with a velocity 3 m/s. The water then enters into a tube of diameter 2 cm. The velocity of water in the other pipe is
(1) 3 m/s
(2) 6 m/s
(3) 12 m/s
(4) 8 m/s
A manometer connected to a closed tap reads pascal. When the tap is opened the reading of the manometer falls to pascal. Then the velocity of flow of water is
1. 7 2. 8
3. 9 4. 10
What is the velocity v of a metallic ball of radius r falling in a tank of liquid at the instant when its acceleration is one-half that of a freely falling body ? (The densities of metal and of liquid are and respectively, and the viscosity of the liquid is ).
(1)
(2)
(3)
(4)
An incompressible fluid flows steadily through a cylindrical pipe which has a radius 2r at point A and a radius r at B further along the flow direction. If the velocity at point A is v, its velocity at point B is:
1. 2v
2. v
3. v/2
4. 4v
A lead shot of 1mm diameter falls through a long column of glycerine. The variation of its velocity v with distance covered is represented by
The surface tension of liquid is 0.5 N/m. If a film is held on a ring of area 0.02 , its surface energy is
(a) (b)
(c) (d)
A mercury drop of radius 1cm is sprayed into drops of equal size. The energy expended in joules is (surface tension of Mercury is )
(1) 0.057
(2) 5.7
(3)
(4)
A water film is formed between the two straight parallel wires, each of length \(10~\text{cm}\), kept at a separation of \(0.5~\text{cm}.\)Now, the separation between them is increased by \(1~\text{mm}\) without breaking the water film. The work done for this is
(surface tension of water =\(7.2\times 10^{-2}~\text{N/m}\))
1. \(7.22\times 10^{-6}~\text{J}\)
2. \(1.44\times 10^{-5}~\text{J}\)
3. \(2.88\times 10^{-5}~\text{J}\)
4. \(5.76\times 10^{-5}~\text{J}\)
A drop of mercury of radius 2 mm is split into 8 identical droplets. Find the increase in surface energy. (Surface tension of mercury is )
(1)
(2)
(3)
(4)
Two small drops of mercury, each of radius r, coalesce to form a single large drop. The ratio of the total surface energies before and after the change is
1.
2.
3. 2:1
4. 1:2
The radius of a soap bubble is increased from R to 2R. Work done in this process in terms of surface tension is
(1)
(2)
(3)
(4)
The work done in blowing a soap bubble of radius 0.2 m is (the surface tension of soap solution being 0.06 N/m)
(1)
(2)
(3)
(4) None of these
A liquid film is formed in a loop of area 0.05 . Increase in its potential energy will be (T = 0.2 N/m)
(1)
(2)
(3)
(4) None of these
In order to float a ring of area 0.04 in a liquid of surface tension 75 N/m, the required surface energy will be
(a) 3 J (b) 6.5 J
(c) 1.5 J (d) 4 J
When a large bubble rises from the bottom of a lake to the surface, its radius doubles. If atmospheric pressure is equal to that of a column of water height H, then the depth of the lake is
(1) H
(2) 2H
(3) 7H
(4) 8H
If pressure at half the depth of a lake is equal to 2/3 pressure at the bottom of the lake then what is the depth of the lake
(1) 10m
(2) 20m
(3) 60m
(4) 30m
Aspherical drop of water has a radius of 1 mm If the surface tension of water is N/m difference of pressures between inside and outside of the spherical drop is
(1)
(2)
(3)
(4) Zero
Two bubbles A and B are joined through a narrow tube where bubble A is bigger. Then
1. The size of A will increase
2. The size of B will increase
3. The size of B will increase until the pressure equals
4. None of these
Two soap bubbles have different radii but their surface tension is the same. Mark the correct statement
(1) Internal pressure of the smaller bubble is higher than the internal pressure of the larger bubble
(2) Pressure of the larger bubble is higher than the smaller bubble
(3) Both bubbles have the same internal pressure
(4) None of the above
If the excess pressure inside a soap bubble is balanced by oil column of height 2 mm, then the surface tension of soap solution will be (r = 1 cm and density d = 0.8 gm/cc)
(1) 3.9 N/m
(2)
(3)
(4) 3.9 dyne/m