Class Assignment [ For IIT JEE 2013 Batch ] Topic: Fluid Statics
PHYSICS
OBJECTIVE TYPE QUESTIONS 1.
The three vessels shown in figure have same base area. Equal volumes of a liquid are poured in the three vessels. The force on the base will be (A) Maximum in vessel A (B) Maximum in vessel B
Vessel A
(C) Maximum in vessel C
Vessel B
(D) equal in all the vessels 2.
Vessel C [HCV]
Equal mass of three liquids are kept in three identical cylindrical vessels A, B and C. The densities are A , B , C and A B C . The force on the base will be
3.
(A) maximum in vessel A
(B) maximum in vessel B
(C) maximum in vessel C
(D) equal in all the vessel
A U – tube having horizontal arm of length 20 cm, has uniform cross-sectional area = 1cm2. It is filled with water of volume 60 cc. What volume of a liquid of density 4 g/cc should be poured from one side into the U – tube so that no water is left in the horizontal arm of the tube? (A) 60 cc
4.
5.
6.
[HCV]
(B) 45 cc
(C) 50 cc
(D) 35 cc
The area of cross-section of the wider tube shown in figure is 800 cm2. If a mass of 12 kg is placed on the massless piston, the difference in heights h in the level of water in the two tubes is : (A) 10 cm
(B) 6 cm
(C) 15 cm
(D) 2 cm
A light semi cylindrical gate of radius R is piovted at its mid point O, of the diameter as shown in the figure holding liquid of density . The force F required to prevent the rotation of the gate is equal to (A) 2R3g
(B) 2gR3l
2 R 2 lg (C) 3
(D) zero
In the figure shown, the heavy cylinder (radius R) resting on a smooth surface separates two liquids of densities 2 and 3. The height ‘h’ for the equilibrium of cylinder must be
3 2
(A) 3R/2
(B) R
(C) R 2
(D) None
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Class Assignment [ For IIT JEE 2013 Batch ] Topic: Fluid Statics
PHYSICS 7.
8.
P1
.
A closed rectangular vessel completely filled with a liquid of densitt moves with an acceleration a. The value of the pressure difference (P1 – P2) is : g b h 2
(A) gb
(B)
(C) ab gh
(D) gh
b
a
h
.
P2
The vessel shown in the figure has two sections. The lower part is a rectangular vessel with area of cross-section A and height h. The upper part is a conical vessel of height h with base area ‘A’ and top area ‘a’ and the walls of the vessel are inclined at an angle 30° with the vertical. A liquid of density fills both the sections upto a height 2h. Neglecting atmospheric pressure. (A) The force F exerted by the liquid on the base of the vessel is 2hg
(B) the pressure P at the base of the vessel is 2hg
(A a ) 2
A a
(C) the weight of the liquid W is greater than the force exerted by the liquid on the base (D) the walls of the vessel exert a downward force (F–W) on the liquid. 9.
10.
Figure shows a three arm tube in which a liquid is filled upto levels of height l. It is now rotated at an angular frequency about an axis passing through arm B. The angular frequency at which level of liquid in arm B becomes zero. (A)
2g 3l
(B)
g l
(C)
3g l
(D)
3g 2l
An open cubical tank was initially fully filled with water. When the tank was accelerated on a horizontal plane along one of its side it was found that one third of volume of water spilled out. The acceleration was (A) g/3
11.
(B) 2g/3
(C) 3g/2
(D) None
A wooden object floats in water kept in a beaker. The object is near a side of the beaker (figure). Let P1, P2, P3 be the pressure at the three points A, B and C of the bottom as shown in the figure. (A) P1 = P2 = P3
(B) P1 < P2 < P3
(C) P1 > P2 > P3
(D) P2 = P3 P1
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[HCV]
2
A
B
C
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Class Assignment [ For IIT JEE 2013 Batch ] Topic: Fluid Statics
PHYSICS 12.
A metal cube is placed in an empty vessel. When water is filled in the vessel so that the cube is completely immersed in the water, the force on the bottom of the vessel in contact with the cube (A) will increase
13.
14.
(B) will decrease
(C) will remain the same
(D) will become zero
[HCV]
A piece of wood is floating in water kept in a bottle. The bottle is connected to an air pump. Neglect the compressibility of water. When more air is pushed into the bottle from the pump, the piece of wood will float with (A) larger part in the water
(B) lesser part in the water
(C) same part in the water
(D) it will sink
[HCV]
A solid floats in a liquid in a partially dipped position. (A) The solid exerts a force equal to its weigth on the liquid (B) The liquid exerts a force of buoyancy on the solid which is equal to the weight of the solid (C) The weight of the displaced liquid equals the weight of the solid (D) The weight of the dipped part of the solid is equal to the weight of the displaced liquid
15.
Two cubes of size 1.0 m sides, one of relative density 0.60 and another of relative density = 1.15 are connected by weightless wire and placed in a large tank of water. Under equilibrium the lighter cube will project above the water surface to a height of (A) 50 cm
16.
(C)
4 gHR2 3
(C) 10 cm
(D) zero
(B) HR2 (D)
2 gHR2 3
A homogeneous solid cylinder of length L (L < H/2), cross-sectional area A/5 is immersed such that it floats with its axis vertical at the liquid-liquid interface with length L/4 in the denser liquid as shown in the figure. The lower density liquid is open to atmosphere having pressure P0. Then, density D of solid is given by [1995, IIT] (A) 5d/4
18.
(B) 25 cm
A cone of radius R and height H, is hanging inside a liquid of density by means of a string as shown in the figure. The force, due to the liquid acting on the slant surface of the cone is (A) gHR2
17.
[HCV]
(B) 4d/5
(C) 4d
(D) d/5
A hemispherical portion of radius R is removed from the bottom of a cylinder of radius R. The volume of the remaining cylinder is V and mass M. It is suspended by a string in a liquid of density , where it stays vertical. The upper surface of the cylinder is at a depth h below the liquid surface. The force on the bottom of the cylinder by the liquid is [2001-IIT] (A) Mg
(B) Mg – Vg
(C) Mg + R2hg
(D) g(V + R2h)
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Class Assignment [ For IIT JEE 2013 Batch ] Topic: Fluid Statics
PHYSICS SUBJECTIVE TYPE QUESTIONS 1.
The heights of mercury surface in the two arms of the manometer shown in figure are 2 cm and 8 cm. Atmoshperic pressure = 1.01 × 105 N m–2. Find (A) the pressure of the gas in the cylinder and (B) the pressure of mercury at the bottom of the U tube.
gas
[HCV] 2.
A U-shaped tube contains a liquid of density and it is rotated about the line as shown in the figure. Find the difference in the levels of liquid column. [2005, IIT]
3.
The area of cross section of the wider tube shown in figure is 900 cm2. If the boy standing on the piston weighs 45 kg, find the difference in the levels of water in the two tubes. [HCV]
4.
Water is filled in a rectangular tank of size 3m × 2m × 1m. (A) Find the total force exerted by the water on the bottom surface of the tank. (B) Consider a vertical side of area 2m × 1m. Take a horizontal strip of width x metre in this side, situated at a depth of x metre from the surface of water. Find the force by the water on this strip. (C) Find the torque of the force calculated in part (B) about the bottom edge of this side. (D) Find the total torque by the water on the side about the bottom edge. Neglect the atmospheric pressure and take g = 10 m s–2. [HCV]
5.
An ornament weighing 36 g in air, weighs only 34 g in water. Assuming that some copper is mixed with gold to prepare the ornament, find the amount of copper in it. Specific gravity of gold is 19.3 and that of copper is 8.9. [HCV]
6.
A cube of ice floats partly in water and partly in K.oil (figure). Find the ratio of the volume of ice immersed in water to that in K. oil. Specific gravity of K.oil is 0.8 and that of ice of 0.9. [HCV]
K.oil Water
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Class Assignment [ For IIT JEE 2013 Batch ] Topic: Fluid Statics
PHYSICS 7.
A cubical block of ice floating in water has to support a metal piece weighing 0.5 kg. What can be the minimum edge of the block so that it does not sink in water? Specific gravity of ice = 0.9. [HCV]
8.
A metal piece of mass 160 g lies in equilibrium inside a glass of water (figure). The piece touches the bottom of the glass at a small number of points. If the density of the metal is 8000 kg m–3, find the normal force exerted by the bottom of the glass on the metal piece. [HCV]
9.
A wooden plank of length 1 m and uniform cross-section is hinged at one end to the bottom of a tank as shown in figure. The tank is filled with water upto a height 0.5 m. The specific gravity of the plank is 0.5. Find the angle that the plank makes with the vertical in the equilibrium position. (exclude the case = 0°) [1984,IIT]
10.
A cubical block of wood weighing 200 g has a lead piece fastened underneath. Find the mass of the lead piece which will just allow the block to float in water. Specific gravity of wood is 0.8 and that of lead is 11.3. [HCV]
11.
Solve the previous problem if the lead piece is fastened on the top surface of the block and the block is to float with its upper surface just dipping into water. [HCV]
12.
A solid sphere of radius 5 cm floats in water. If a maximum load of 0.1 kg can be put on it without wetting the load, find the specific gravity of the material of the sphere. [HCV]
13.
A cube of ice of edge 4 cm is placed in an empty cylindrical glass of inner diameter 6 cm. Assume that the ice melts uniformly from each side so that it always retains its cubical shape. Remembering that ice is lighter than water, find the length of the edge of the ice cube at the instant it just leaves contact with the bottom of the glass. [HCV]
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Class Assignment [ For IIT JEE 2013 Batch ] Topic: Fluid Statics
PHYSICS
ANSWERS KEY OBJECTIVE 1. (C)
2. (D)
3. (D)
4. (C)
5. (D)
6. (B)
7. (C)
8. (D)
9. (C)
10. (C)
11. (A)
12. (C)
13. (C)
14. (A, B, C)
15. (B)
16. (D)
17. (A)
18. (D)
SUBJECTIVE 1. (a) 1.09 × 105 N m–2, (b) 1.12 × 105 N m–2
3. 50 cm
4. (a) 60000 N, (b) 20000 x dx N, (c) 20000 × (1 – x)dx N-m, (d) 10000 N, (e) 10000/3 N-m 5. 2.2 g
6. 1 : 1
7. 17 cm
8. 1.4 N
10. 54.8 g
11. 50 g
12. 0.8
13. 2.26 cm
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