DC Pandey Solutions (JEE Main): Fluid Mechanics | DC Pandey Solutions for JEE Physics PDF Download

 Page 1


EXERCISES 
For JEE Main 
  Subjective Questions 
  Upthrust 
Q 1.  A block of material has a density ?1
 
and floats three-fourth submerged in a liquid of unknown 
density. Show that the density ?2
 
of the unknown liquid is given by 
21
4
3
? ? ? .
 
 
Q 2.  A metal ball weighs 0.096 N. When suspended in water it has an apparent weight of 0.071 N. Find 
the density of the metal. 
Q 3.  A block of wood has a mass of 25 g. When a 5 g metal piece with a volume of 2 cm is attached to 
the bottom of the block, the wood barely floats in water. What is the volume V of the wood? 
Q 4.  A block of wood weighing 71.2 N and of specific gravity 0.75 is tied by a string to the bottom of a 
tank of water in order to have the block totally immersed. What is the tension in the string? 
Q 5.  What is the minimum volume of a block of wood (density = 850 kg/m
3
) if it is to hold a 50 kg 
woman entirely above the water when she stands on it ? 
Q 6.  An irregular piece of metal weighs 10.00 g in air and 8.00 g when submerged in water. 
  (a) Find the volume of the metal and its density. 
(b) If the same piece of metal weighs 8.50 g when immersed in a particular oil, what is the density 
of the oil ? 
Q 7.  A beaker when partly filled with water has total mass 20.00 g. If a piece of metal with density 3.00 
g/cm
3
 and volume 1.00 cm is suspended by a thin string, so that it is submerged in the water but 
does not rest on the bottom of the beaker, how much does the beaker then appear to weigh if it is 
resting on a scale? 
Q 8.  A tank contains water on top of mercury. A cube of iron, 60 mm along each edge, is sitting upright 
in equilibrium in the liquids. Find how much of it is in each liquid. The densities of iron and 
mercury are 7.7 × 10
3
 kg/m
3
 and 13.6
 
× 10
3
 kg/m
3
 respectively. 
 
Q 9.  A small block of wood, of density 0.4 × 10
3
 kg/m
3
, is submerged in water at a depth of 2.9 m. 
  Find: 
  (a) the acceleration of the block toward the surface when the block is released and 
  (b) the time for the block to reach the surface. Ignore viscosity. 
Q 10.  A uniform rod AB, 4 m long and weighing 12 kg, is supported at end A, with a 6 kg lead weight at 
B. The rod floats as shown in figure with one-half of its length submerged. The buoyant force on 
Page 2


EXERCISES 
For JEE Main 
  Subjective Questions 
  Upthrust 
Q 1.  A block of material has a density ?1
 
and floats three-fourth submerged in a liquid of unknown 
density. Show that the density ?2
 
of the unknown liquid is given by 
21
4
3
? ? ? .
 
 
Q 2.  A metal ball weighs 0.096 N. When suspended in water it has an apparent weight of 0.071 N. Find 
the density of the metal. 
Q 3.  A block of wood has a mass of 25 g. When a 5 g metal piece with a volume of 2 cm is attached to 
the bottom of the block, the wood barely floats in water. What is the volume V of the wood? 
Q 4.  A block of wood weighing 71.2 N and of specific gravity 0.75 is tied by a string to the bottom of a 
tank of water in order to have the block totally immersed. What is the tension in the string? 
Q 5.  What is the minimum volume of a block of wood (density = 850 kg/m
3
) if it is to hold a 50 kg 
woman entirely above the water when she stands on it ? 
Q 6.  An irregular piece of metal weighs 10.00 g in air and 8.00 g when submerged in water. 
  (a) Find the volume of the metal and its density. 
(b) If the same piece of metal weighs 8.50 g when immersed in a particular oil, what is the density 
of the oil ? 
Q 7.  A beaker when partly filled with water has total mass 20.00 g. If a piece of metal with density 3.00 
g/cm
3
 and volume 1.00 cm is suspended by a thin string, so that it is submerged in the water but 
does not rest on the bottom of the beaker, how much does the beaker then appear to weigh if it is 
resting on a scale? 
Q 8.  A tank contains water on top of mercury. A cube of iron, 60 mm along each edge, is sitting upright 
in equilibrium in the liquids. Find how much of it is in each liquid. The densities of iron and 
mercury are 7.7 × 10
3
 kg/m
3
 and 13.6
 
× 10
3
 kg/m
3
 respectively. 
 
Q 9.  A small block of wood, of density 0.4 × 10
3
 kg/m
3
, is submerged in water at a depth of 2.9 m. 
  Find: 
  (a) the acceleration of the block toward the surface when the block is released and 
  (b) the time for the block to reach the surface. Ignore viscosity. 
Q 10.  A uniform rod AB, 4 m long and weighing 12 kg, is supported at end A, with a 6 kg lead weight at 
B. The rod floats as shown in figure with one-half of its length submerged. The buoyant force on 
the lead mass is negligible as it is of negligible volume. Find the tension in the cord and the total 
volume of the rod. 
 
Q 11.  A solid sphere of mass m = 2 kg and density ?
 
= 500 kg/m is held stationary relative to a tank 
filled with water. The tank is accelerating upward with acceleration 2 m/s
2
. Calculate : 
 
  (a) Tension in the thread connected between the sphere and the bottom of the tank. 
(b) If the thread snaps, calculate the acceleration of sphere with respect to the tank.  
[Density of water = 1000 kg/m
3
, g = 10m/s
2
] 
  Pressure and Pascal’s Law 
Q 12.  The pressure gauge shown in figure has a spring for which k = 60N/m and the area of the piston is 
0.50 cm
2
. Its right end is connected to a closed container of gas at a gauge pressure of 30 kPa. 
How far will the spring be compressed if the region containing the spring is  
  (a) in vacuum and (b) open to the atmosphere ? Atmospheric pressure is 101 kPa. 
 
Q 13.  A small uniform tube is bent into a circle of radius r whose plane is vertical. Equal volumes of two 
fluids whose densities are ? and ?( ? > ?)
 
fill half the circle. Find the angle that the radius passing 
through the interface makes with the vertical. 
 
Q 14.  For the system shown in figure, the cylinder on the left, at L, has a mass of 600 kg and a cross-
sectional area of 800 cm . The piston on the right, at S, has cross-sectional area 25 cm and 
negligible weight. If the apparatus is filled with oil ( ?
 
= 0.78 g/cm
3
), what is the force F required 
to hold the system in equilibrium ? 
Page 3


EXERCISES 
For JEE Main 
  Subjective Questions 
  Upthrust 
Q 1.  A block of material has a density ?1
 
and floats three-fourth submerged in a liquid of unknown 
density. Show that the density ?2
 
of the unknown liquid is given by 
21
4
3
? ? ? .
 
 
Q 2.  A metal ball weighs 0.096 N. When suspended in water it has an apparent weight of 0.071 N. Find 
the density of the metal. 
Q 3.  A block of wood has a mass of 25 g. When a 5 g metal piece with a volume of 2 cm is attached to 
the bottom of the block, the wood barely floats in water. What is the volume V of the wood? 
Q 4.  A block of wood weighing 71.2 N and of specific gravity 0.75 is tied by a string to the bottom of a 
tank of water in order to have the block totally immersed. What is the tension in the string? 
Q 5.  What is the minimum volume of a block of wood (density = 850 kg/m
3
) if it is to hold a 50 kg 
woman entirely above the water when she stands on it ? 
Q 6.  An irregular piece of metal weighs 10.00 g in air and 8.00 g when submerged in water. 
  (a) Find the volume of the metal and its density. 
(b) If the same piece of metal weighs 8.50 g when immersed in a particular oil, what is the density 
of the oil ? 
Q 7.  A beaker when partly filled with water has total mass 20.00 g. If a piece of metal with density 3.00 
g/cm
3
 and volume 1.00 cm is suspended by a thin string, so that it is submerged in the water but 
does not rest on the bottom of the beaker, how much does the beaker then appear to weigh if it is 
resting on a scale? 
Q 8.  A tank contains water on top of mercury. A cube of iron, 60 mm along each edge, is sitting upright 
in equilibrium in the liquids. Find how much of it is in each liquid. The densities of iron and 
mercury are 7.7 × 10
3
 kg/m
3
 and 13.6
 
× 10
3
 kg/m
3
 respectively. 
 
Q 9.  A small block of wood, of density 0.4 × 10
3
 kg/m
3
, is submerged in water at a depth of 2.9 m. 
  Find: 
  (a) the acceleration of the block toward the surface when the block is released and 
  (b) the time for the block to reach the surface. Ignore viscosity. 
Q 10.  A uniform rod AB, 4 m long and weighing 12 kg, is supported at end A, with a 6 kg lead weight at 
B. The rod floats as shown in figure with one-half of its length submerged. The buoyant force on 
the lead mass is negligible as it is of negligible volume. Find the tension in the cord and the total 
volume of the rod. 
 
Q 11.  A solid sphere of mass m = 2 kg and density ?
 
= 500 kg/m is held stationary relative to a tank 
filled with water. The tank is accelerating upward with acceleration 2 m/s
2
. Calculate : 
 
  (a) Tension in the thread connected between the sphere and the bottom of the tank. 
(b) If the thread snaps, calculate the acceleration of sphere with respect to the tank.  
[Density of water = 1000 kg/m
3
, g = 10m/s
2
] 
  Pressure and Pascal’s Law 
Q 12.  The pressure gauge shown in figure has a spring for which k = 60N/m and the area of the piston is 
0.50 cm
2
. Its right end is connected to a closed container of gas at a gauge pressure of 30 kPa. 
How far will the spring be compressed if the region containing the spring is  
  (a) in vacuum and (b) open to the atmosphere ? Atmospheric pressure is 101 kPa. 
 
Q 13.  A small uniform tube is bent into a circle of radius r whose plane is vertical. Equal volumes of two 
fluids whose densities are ? and ?( ? > ?)
 
fill half the circle. Find the angle that the radius passing 
through the interface makes with the vertical. 
 
Q 14.  For the system shown in figure, the cylinder on the left, at L, has a mass of 600 kg and a cross-
sectional area of 800 cm . The piston on the right, at S, has cross-sectional area 25 cm and 
negligible weight. If the apparatus is filled with oil ( ?
 
= 0.78 g/cm
3
), what is the force F required 
to hold the system in equilibrium ? 
 
Q 15.  A U-tube of uniform cross-sectional area and open to the atmosphere is partially filled with 
mercury. Water is then poured into both arms. If the equilibrium configuration of the tube is as 
shown in figure with h2 = 1.0 cm, determine the value of h1. 
 
Q 16.  Water stands at a depth h behind the vertical face of a dam. It exerts a resultant horizontal force on 
the dam tending to slide it along its foundation and a torque tending to overturn the dam about the 
point O. Find : 
 
  (a) horizontal force,  (b) torque about O, 
(c) the height at which the resultant force would have to act to produce the same torque, l = cross-
sectional length and ? = density of water. 
Q 17.  A U-shaped tube open to the air at both ends contains some mercury. A quantity of water is 
carefully poured into the left arm of the U-shaped tube until the vertical height of the water 
column is 15.0 cm. 
  (a) What is the gauge pressure at the water mercury interface ? 
(b) Calculate the vertical distance h from the top of the mercury in the right hand arm of the tube 
to the top of the water in the left-hand arm, 
 
Q 18.  Water and oil are poured into the two limbs of a U-tube containing mercury. The interfaces of the 
mercury and the liquids are at the same height in both limbs. 
Page 4


EXERCISES 
For JEE Main 
  Subjective Questions 
  Upthrust 
Q 1.  A block of material has a density ?1
 
and floats three-fourth submerged in a liquid of unknown 
density. Show that the density ?2
 
of the unknown liquid is given by 
21
4
3
? ? ? .
 
 
Q 2.  A metal ball weighs 0.096 N. When suspended in water it has an apparent weight of 0.071 N. Find 
the density of the metal. 
Q 3.  A block of wood has a mass of 25 g. When a 5 g metal piece with a volume of 2 cm is attached to 
the bottom of the block, the wood barely floats in water. What is the volume V of the wood? 
Q 4.  A block of wood weighing 71.2 N and of specific gravity 0.75 is tied by a string to the bottom of a 
tank of water in order to have the block totally immersed. What is the tension in the string? 
Q 5.  What is the minimum volume of a block of wood (density = 850 kg/m
3
) if it is to hold a 50 kg 
woman entirely above the water when she stands on it ? 
Q 6.  An irregular piece of metal weighs 10.00 g in air and 8.00 g when submerged in water. 
  (a) Find the volume of the metal and its density. 
(b) If the same piece of metal weighs 8.50 g when immersed in a particular oil, what is the density 
of the oil ? 
Q 7.  A beaker when partly filled with water has total mass 20.00 g. If a piece of metal with density 3.00 
g/cm
3
 and volume 1.00 cm is suspended by a thin string, so that it is submerged in the water but 
does not rest on the bottom of the beaker, how much does the beaker then appear to weigh if it is 
resting on a scale? 
Q 8.  A tank contains water on top of mercury. A cube of iron, 60 mm along each edge, is sitting upright 
in equilibrium in the liquids. Find how much of it is in each liquid. The densities of iron and 
mercury are 7.7 × 10
3
 kg/m
3
 and 13.6
 
× 10
3
 kg/m
3
 respectively. 
 
Q 9.  A small block of wood, of density 0.4 × 10
3
 kg/m
3
, is submerged in water at a depth of 2.9 m. 
  Find: 
  (a) the acceleration of the block toward the surface when the block is released and 
  (b) the time for the block to reach the surface. Ignore viscosity. 
Q 10.  A uniform rod AB, 4 m long and weighing 12 kg, is supported at end A, with a 6 kg lead weight at 
B. The rod floats as shown in figure with one-half of its length submerged. The buoyant force on 
the lead mass is negligible as it is of negligible volume. Find the tension in the cord and the total 
volume of the rod. 
 
Q 11.  A solid sphere of mass m = 2 kg and density ?
 
= 500 kg/m is held stationary relative to a tank 
filled with water. The tank is accelerating upward with acceleration 2 m/s
2
. Calculate : 
 
  (a) Tension in the thread connected between the sphere and the bottom of the tank. 
(b) If the thread snaps, calculate the acceleration of sphere with respect to the tank.  
[Density of water = 1000 kg/m
3
, g = 10m/s
2
] 
  Pressure and Pascal’s Law 
Q 12.  The pressure gauge shown in figure has a spring for which k = 60N/m and the area of the piston is 
0.50 cm
2
. Its right end is connected to a closed container of gas at a gauge pressure of 30 kPa. 
How far will the spring be compressed if the region containing the spring is  
  (a) in vacuum and (b) open to the atmosphere ? Atmospheric pressure is 101 kPa. 
 
Q 13.  A small uniform tube is bent into a circle of radius r whose plane is vertical. Equal volumes of two 
fluids whose densities are ? and ?( ? > ?)
 
fill half the circle. Find the angle that the radius passing 
through the interface makes with the vertical. 
 
Q 14.  For the system shown in figure, the cylinder on the left, at L, has a mass of 600 kg and a cross-
sectional area of 800 cm . The piston on the right, at S, has cross-sectional area 25 cm and 
negligible weight. If the apparatus is filled with oil ( ?
 
= 0.78 g/cm
3
), what is the force F required 
to hold the system in equilibrium ? 
 
Q 15.  A U-tube of uniform cross-sectional area and open to the atmosphere is partially filled with 
mercury. Water is then poured into both arms. If the equilibrium configuration of the tube is as 
shown in figure with h2 = 1.0 cm, determine the value of h1. 
 
Q 16.  Water stands at a depth h behind the vertical face of a dam. It exerts a resultant horizontal force on 
the dam tending to slide it along its foundation and a torque tending to overturn the dam about the 
point O. Find : 
 
  (a) horizontal force,  (b) torque about O, 
(c) the height at which the resultant force would have to act to produce the same torque, l = cross-
sectional length and ? = density of water. 
Q 17.  A U-shaped tube open to the air at both ends contains some mercury. A quantity of water is 
carefully poured into the left arm of the U-shaped tube until the vertical height of the water 
column is 15.0 cm. 
  (a) What is the gauge pressure at the water mercury interface ? 
(b) Calculate the vertical distance h from the top of the mercury in the right hand arm of the tube 
to the top of the water in the left-hand arm, 
 
Q 18.  Water and oil are poured into the two limbs of a U-tube containing mercury. The interfaces of the 
mercury and the liquids are at the same height in both limbs. 
Determine the height of the water column h1 if that of the oil h 2 = 20 cm. The density of the oil is 
0.9. 
 
Q 19.  Mercury is poured into a U-tube in which the cross-sectional area of the left-hand limb is three 
times smaller than that of the right one. The level of the mercury in the narrow limb is a distance / 
= 30 cm from the upper end of the tube. How much will the mercury level rise in the right-hand 
limb if the left one is filled to the top with water ? 
  Fluids in Motion 
Q 20.  Water is flowing smoothly through a closed-pipe system. At one point the speed of the water is 3.0 
m/s, while at another point 1.0 m higher the speed is 4.0 m/s. If the pressure is 20 kPa at the lower 
point, what is the pressure at the upper point ? What would the pressure at the upper point be if the 
water were to stop flowing and the pressure at the lower point were 18 kPa ? 
Q 21.  A water barrel stands on a table of height h. If a small hole is punched in the side of the barrel at 
its base, it is found that the resultant stream of water strikes the ground at a horizontal distance R 
from the barrel. What is the depth of water in the barrel ? 
Q 22.  A pump is designed as a horizontal cylinder with a piston of area A and an outlet orifice of area a 
arranged near the cylinder axis. Find the velocity of out flow of the liquid from the pump if the 
piston moves with a constant velocity under the action of a constant force F. The density of the 
liquid is ?.
  
Q 23.  When air of density 1.3 kg/m
3
 flows across the top of the tube shown in the accompanying figure, 
water rises in the tube to a height of 1.0 cm. What is the speed of the air ? 
 
Q 24.  The area of cross-section of a large tank is 0.5 m
2
. It has an opening near the bottom having area 
of cross-section 1 cm . A load of 20 kg is applied on the water at the top. Find the velocity of the 
water coming out of the opening at the time when the height of water level is 50 cm above the 
bottom.  (Take g = 10m/s
2
) 
Q 25.  Water flows through a horizontal tube as shown in figure . If the difference of heights of water 
column in the vertical tubes is 2 cm and the areas of cross-section at A and B are 4 cm
2
 and 2 cm
2 
respectively. Find the rate of flow of water across any section. 
Page 5


EXERCISES 
For JEE Main 
  Subjective Questions 
  Upthrust 
Q 1.  A block of material has a density ?1
 
and floats three-fourth submerged in a liquid of unknown 
density. Show that the density ?2
 
of the unknown liquid is given by 
21
4
3
? ? ? .
 
 
Q 2.  A metal ball weighs 0.096 N. When suspended in water it has an apparent weight of 0.071 N. Find 
the density of the metal. 
Q 3.  A block of wood has a mass of 25 g. When a 5 g metal piece with a volume of 2 cm is attached to 
the bottom of the block, the wood barely floats in water. What is the volume V of the wood? 
Q 4.  A block of wood weighing 71.2 N and of specific gravity 0.75 is tied by a string to the bottom of a 
tank of water in order to have the block totally immersed. What is the tension in the string? 
Q 5.  What is the minimum volume of a block of wood (density = 850 kg/m
3
) if it is to hold a 50 kg 
woman entirely above the water when she stands on it ? 
Q 6.  An irregular piece of metal weighs 10.00 g in air and 8.00 g when submerged in water. 
  (a) Find the volume of the metal and its density. 
(b) If the same piece of metal weighs 8.50 g when immersed in a particular oil, what is the density 
of the oil ? 
Q 7.  A beaker when partly filled with water has total mass 20.00 g. If a piece of metal with density 3.00 
g/cm
3
 and volume 1.00 cm is suspended by a thin string, so that it is submerged in the water but 
does not rest on the bottom of the beaker, how much does the beaker then appear to weigh if it is 
resting on a scale? 
Q 8.  A tank contains water on top of mercury. A cube of iron, 60 mm along each edge, is sitting upright 
in equilibrium in the liquids. Find how much of it is in each liquid. The densities of iron and 
mercury are 7.7 × 10
3
 kg/m
3
 and 13.6
 
× 10
3
 kg/m
3
 respectively. 
 
Q 9.  A small block of wood, of density 0.4 × 10
3
 kg/m
3
, is submerged in water at a depth of 2.9 m. 
  Find: 
  (a) the acceleration of the block toward the surface when the block is released and 
  (b) the time for the block to reach the surface. Ignore viscosity. 
Q 10.  A uniform rod AB, 4 m long and weighing 12 kg, is supported at end A, with a 6 kg lead weight at 
B. The rod floats as shown in figure with one-half of its length submerged. The buoyant force on 
the lead mass is negligible as it is of negligible volume. Find the tension in the cord and the total 
volume of the rod. 
 
Q 11.  A solid sphere of mass m = 2 kg and density ?
 
= 500 kg/m is held stationary relative to a tank 
filled with water. The tank is accelerating upward with acceleration 2 m/s
2
. Calculate : 
 
  (a) Tension in the thread connected between the sphere and the bottom of the tank. 
(b) If the thread snaps, calculate the acceleration of sphere with respect to the tank.  
[Density of water = 1000 kg/m
3
, g = 10m/s
2
] 
  Pressure and Pascal’s Law 
Q 12.  The pressure gauge shown in figure has a spring for which k = 60N/m and the area of the piston is 
0.50 cm
2
. Its right end is connected to a closed container of gas at a gauge pressure of 30 kPa. 
How far will the spring be compressed if the region containing the spring is  
  (a) in vacuum and (b) open to the atmosphere ? Atmospheric pressure is 101 kPa. 
 
Q 13.  A small uniform tube is bent into a circle of radius r whose plane is vertical. Equal volumes of two 
fluids whose densities are ? and ?( ? > ?)
 
fill half the circle. Find the angle that the radius passing 
through the interface makes with the vertical. 
 
Q 14.  For the system shown in figure, the cylinder on the left, at L, has a mass of 600 kg and a cross-
sectional area of 800 cm . The piston on the right, at S, has cross-sectional area 25 cm and 
negligible weight. If the apparatus is filled with oil ( ?
 
= 0.78 g/cm
3
), what is the force F required 
to hold the system in equilibrium ? 
 
Q 15.  A U-tube of uniform cross-sectional area and open to the atmosphere is partially filled with 
mercury. Water is then poured into both arms. If the equilibrium configuration of the tube is as 
shown in figure with h2 = 1.0 cm, determine the value of h1. 
 
Q 16.  Water stands at a depth h behind the vertical face of a dam. It exerts a resultant horizontal force on 
the dam tending to slide it along its foundation and a torque tending to overturn the dam about the 
point O. Find : 
 
  (a) horizontal force,  (b) torque about O, 
(c) the height at which the resultant force would have to act to produce the same torque, l = cross-
sectional length and ? = density of water. 
Q 17.  A U-shaped tube open to the air at both ends contains some mercury. A quantity of water is 
carefully poured into the left arm of the U-shaped tube until the vertical height of the water 
column is 15.0 cm. 
  (a) What is the gauge pressure at the water mercury interface ? 
(b) Calculate the vertical distance h from the top of the mercury in the right hand arm of the tube 
to the top of the water in the left-hand arm, 
 
Q 18.  Water and oil are poured into the two limbs of a U-tube containing mercury. The interfaces of the 
mercury and the liquids are at the same height in both limbs. 
Determine the height of the water column h1 if that of the oil h 2 = 20 cm. The density of the oil is 
0.9. 
 
Q 19.  Mercury is poured into a U-tube in which the cross-sectional area of the left-hand limb is three 
times smaller than that of the right one. The level of the mercury in the narrow limb is a distance / 
= 30 cm from the upper end of the tube. How much will the mercury level rise in the right-hand 
limb if the left one is filled to the top with water ? 
  Fluids in Motion 
Q 20.  Water is flowing smoothly through a closed-pipe system. At one point the speed of the water is 3.0 
m/s, while at another point 1.0 m higher the speed is 4.0 m/s. If the pressure is 20 kPa at the lower 
point, what is the pressure at the upper point ? What would the pressure at the upper point be if the 
water were to stop flowing and the pressure at the lower point were 18 kPa ? 
Q 21.  A water barrel stands on a table of height h. If a small hole is punched in the side of the barrel at 
its base, it is found that the resultant stream of water strikes the ground at a horizontal distance R 
from the barrel. What is the depth of water in the barrel ? 
Q 22.  A pump is designed as a horizontal cylinder with a piston of area A and an outlet orifice of area a 
arranged near the cylinder axis. Find the velocity of out flow of the liquid from the pump if the 
piston moves with a constant velocity under the action of a constant force F. The density of the 
liquid is ?.
  
Q 23.  When air of density 1.3 kg/m
3
 flows across the top of the tube shown in the accompanying figure, 
water rises in the tube to a height of 1.0 cm. What is the speed of the air ? 
 
Q 24.  The area of cross-section of a large tank is 0.5 m
2
. It has an opening near the bottom having area 
of cross-section 1 cm . A load of 20 kg is applied on the water at the top. Find the velocity of the 
water coming out of the opening at the time when the height of water level is 50 cm above the 
bottom.  (Take g = 10m/s
2
) 
Q 25.  Water flows through a horizontal tube as shown in figure . If the difference of heights of water 
column in the vertical tubes is 2 cm and the areas of cross-section at A and B are 4 cm
2
 and 2 cm
2 
respectively. Find the rate of flow of water across any section. 
 
Q 26.  Water flows through the tube as shown in figure. The areas of cross-section of the wide and the 
narrow portions of the tube are 5 cm and 2cm
2
 respectively. The rate of flow of water through the 
tube is 500 cm
3
/s. Find the difference of mercury levels in the U-tube. 
  Viscosity and Surface Tension 
  Note  - 1 Poise = 0.1 N-s/m
2
 and 1 Pl = 1.0 N-s/m
2
. 
Q 27.  A typical river borne silt particle has a radius of 20 ?m and a density of 2 × 10
3
 kg/m
3
. The 
viscosity of water is 1.0 mPl. Find the terminal speed with which such a particle will settle to the 
bottom of a motionless volume of water. 
Q 28.  What is the pressure drop (in mm Hg) in the blood as it passes through a capillary 1 mm long and 
2?m
 
in radius if the speed of the blood through the centre of the capillary is 0.66 mm/s ? (The 
viscosity of whole blood is 4 × 10
-3
 Pl). 
Q 29.  Two equal drops of water are falling through air with a steady velocity v. If the drops coalesced, 
what will be the new velocity ? 
Q 30.  A long cylinder of radius R is displaced along its axis with a constant velocity u0 inside a 
stationary co-axial cylinder of radius R2. The space between the cylinders is filled with viscous 
liquid. Find the velocity of the liquid as a function of the distance r from the axis of the cylinders. 
The flow is laminar. 
Q 31.  A large wooden plate of area 10 m floating on the surface of a river is made to move horizontally 
with a speed of 2 m/s by applying a tangential force. If the river is 1 m deep and the water in 
contact with the bed is stationary, find the tangential force needed to keep the plate moving. 
Coefficient of viscosity of water at the temperature of the river = 10
-2
 poise. 
Q 32.  The velocity of water in a river is 18 km/h near the surface. If the river is 5 m deep, find the 
shearing stress between the horizontal layers of water. The coefficient of viscosity of water = 10
-2
 
poise. 
Q 33.  Water rises up in a glass capillary upto a height of 9.0 cm, while mercury falls down by 3.4 cm in 
the same capillary. Assume angles of contact for water glass and mercury glass 0° and 135° 
respectively. Determine the ratio of surface tension of mercury and water (cos 135° = - 0.71). 
Q 34.  Two equal spherical bubbles of radius a each coalesce to form a spherical bubble of radius b. If P 
is the atmospheric pressure, show that the surface tension of the bubble is 
33
22
P(2a b )
4(b 2a )
?
?
.