CPP REVISION-2 FLUID STATICS

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Single Correct Answer Type:

1. An open cubical tank of side 1m is completely filled with water kept on a horizontal surface. It’s acceleration

is then slowly increased to 22 m/ s . Find the mass of water that would spill out of the tank.

(A) 0.1 kg (B) 10 kg (C) 0.01 kg (D) 100 kg

2. Figure shows a circular tube of small cross section in which equal. Volumes of two

liquids which do not mix into each other are filled. Each liquid occupies one fourth

length of tube. If densities of liquids are and ( ). Find the angle which the

liquid junction makes with vertical at centre in equilibrium state

(A) 1tan

(B) 1tan

(C) 1tan

(D) 1tan

3. Figure shows a J tube of which end A is closed and end B is open. Some mercury is

filled in tube. So that initially levels of mercury in both arms are equal and volume V of

air is trapped in arm A. Find the length of mercury column to be poured in arm B so that

volume of trapped air reduces to v/2. Given that atmospheric pressure is 76 cm of Hg.

(A) 86 cm (B) 96 cm

(C) 76 cm (D) 106 cm

4. When equal volumes of two substances are mixed together. The specific gravity of mixture is 4. But when

equal weights of the same substances are mixed together, the specific gravity of mixture is 3. Find the

specific gravities of the two substances

(A) 1 26 and 2 (B) 1 24 and 3 (C) 1 212 and 1 (D) 1 23 and 4

5. A glass tube of radius 0.8 cm floats vertical in water as shown in figure. What mass of

lead pellets would cause the tube to sink further by 3 cm

(A) 6.03 gm (B) 1 gm

(C) 16.03 gm (D) 0.3 gm

6. A cubical block of wood of edge 3 cm floats in water. The lower surface of

the cube just touches the free end of a vertical spring fixed at the bottom of

the container as shown in figure. Find the maximum weight that can be put

on the block without wetting it. Take density of wood 3800 kg/m and force

constant of spring 50 N/m and 2g 10 m/ s

(A) 0.35 kg (B) 3.5 kg (C) 0.65 kg (D) 6.5 kg

7. A piece of gold weighing 36 gm in air, weight 34 gm in water. If there is some copper impurity in gold. Find

the amount in it. Given that specific gravity of gold is 19.3 and that of copper is 8.9.

(A) 2 gm (B) 2.225 gm (C) 1.775 gm (D) 4 gm

8. Three liquids of densities d, 2d and 3d are mixed in equal proportions of weights. The relative density of the

mixture is

(A) 11d

7 (B)

18 d

11 (C)

13d

9 (D)

23d

18

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9. A triangular lamina of area A and height ‘h’ is immerse in a liquid of density in a vertical plane with its

base on the surface of the liquid. The thrust on the lamina is

(A) 1

A gh2

(B) 1

A gh3

(C) 1

A gh6

(D) 2

A gh3

10. The area of cross-section of wider tube shown in figure is 2800 cm . 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

11. A solid sphere of density n 1 times lighter than water is suspended in a water tank by

a string tied to its base as shown in Fig. If the mass of the sphere is ‘m’, then the

tension in the string is given by

(A) n 1

mgn

(B) nmg

(C) mg

n 1 (D) n 1 mg

12. Two spheres of volume 250 cc each but of relative densities 0.8 and 1.2 are

connected by a string and the combination is immersed in a liquid in vertical

position as shown in figure. The tension in the string is

2g 10 m/s

(A) 5.0 N (B) 0.5 N (C) 1.0 N (D) 2.0 N

13. A homogenous 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 0P . The density ‘D’ of solid is given by

(A) 5

d4

(B) 4

d5

(C) d (D) d

5

14. A log of wood of mass 120 kg floats in water. The weight that can be put on the log to make it just sink,

should be (density of wood 3600 kg/m )

(A) 80 kg (B) 50 kg (C) 60 kg (D) 30 kg

15. A body having volume ‘V’ and density ‘ ’ is attached to the bottom of a container as

shown. Density of the liquid is d container has a constant upward acceleration ‘a’.

Tension in the string is

(A) V dg g a (B) V g a d

(C) V d g (D) None

16. A cubical block is floating in a liquid with 3

4of its volume immersed in the liquid when the whole system

accelerates downwards with a net acceleration of g/4, the fraction of volume immersed in the liquid will be

(A) 1

2 (B)

1

4 (C)

3

4 (D)

3

8

KUKATPALLY CENTRE: # 22-97, Plot No.1, Opp. Patel Kunta Huda Park, Vijaynagar Colony, Hyderabad - 500 072. Ph.: 040-64601123

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17. A cubical block of wood 20.0 cm on a side and density of 3500 kg/m floating on water. From its equilibrium

floating position, it is pushed further by 4.0 cm into the water. What is the force needed to keep the block in

this new position? 2g 10 m/ s

(A) 16 N (B) 32 N (C) 40 N (D) 56 N

18. A solid floats in water with 3/4 of its volume below the surface of water. Calculate the density of solid.

(A) 3750 kg/m (B) 3650 kg/m (C) 3400 kg/m (D) 3300 kg/m

19. A block of wood is floating on water at 0 C with a certain volume ‘V’ above the water level. The temperature

of water is slowly raised from 0 C to 20 C . How will the volume, ‘V’ change with the rise in temperature?

(A) ‘V’ increases with rise in temperature (B) ‘V’ decreases with rise in temperature

(C) No effect (D) None

20. A slender homogeneous rod of length 2L floats partly immersed in water, being

supported by a string fastened to one of its ends, as shown. The specific gravity of

the rod is 0.75. The length of the rod that extends out of the water is

(A) L (B) 1

L2

(C) 1

L4

(D) 3L

Numerical Based:

21. A cube of wood supporting 200 gm mass just floats in water in fully submerged state, When the mass is

removed cube rises by 2 cm above water level. Find the size of the cube 3w 1000 kg/m

22. A piece of copper having an internal cavity weights 264 gm in air and 221 gm in water. Find the volume of

cavity. Take density of copper 38.8 gm/cm

23. In a hydrallic press, used for compressing cotton, the area of the piston is 0.1 m2 and the force exerted

along the piston rod is 200 N. If the area of the larger cylinder is 0.8 m2. Find the total crushing force exerted

on the hale of cotton.

24. A metal piece of mass 1600 gm lies in equilibrium inside a glass of water. The piece touches the bottom of

the glass at a small number of points. If the density of the metal is 3800 kg/m . Find the normal force

exerted by the bottom of the glass on the metal piece.

25. A U-tube contains water and liquid separated by mercury the mercury

columns in the two arms are in level with 10 cm of water in one arm and 5 cm

of liquid in the other. What is the specific gravity of liquid?

KEY

1. D 2. B 3. B 4. A 5. A

6. A 7. B 8. B 9. A 10. C

11. D 12. B 13. A 14. A 15. B

16. C 17. A 18. A 19. B 20. A

21. 10 22. 13 23. 1600 24. 14 25. 2