Hydrostatics Multiple Questions And Answers

Hydrostatics Multiple Questions And Answers

Question 1. Spheres of iron and lead having same mass are com-pletely immersed in water. Density of lead is more than that of iron. Apparent loss of weight is w₂ for iron sphere and w₂ for lead sphere. Then w₁/w₂  is

1. 1
2. Between 0 and 1
3. 0
4. >1

Answer: 4. >1

Question 2. A U-tube of uniform cross-section contains some mercury. In one of its limbs, water is poured and in the other oil is poured such that the mercury in both the limbs remains at the same level. If the heights of the water and oil columns are 0.10 m and 0.125 m respectively, then the specific gravity of the oil will be

1. 0.8
2. 1.0
3. 1.25
4. 0.6

Answer: 1. 0.8

Question 3. The radius of a cylindrical container is r. When a liquid is poured into the container up to a height h, then the thrust on the bottom and that on the lateral surface of the container becomes equal. In this case

1. h = r/2
2. h= r
3. h = 2r
4. h = 4r

Answer: 2. h= r

Question 4. The density ρ of water of bulk modulus B at a depth y in the ocean is related to the density at surface ρ₀ by the relation

1. \(\rho=\rho_0\left(1-\frac{\rho_0 g y}{B}\right)\)
2. \(\rho=\rho_0\left(1+\frac{\rho_0 g y}{B}\right)\)
3. \(\rho=\rho_0\left(1+\frac{B}{\rho_0 g y}\right)\)
4. \(\rho=\rho_0\left(1-\frac{B}{\rho_0 g y}\right)\)

Answer: 2. \(\rho=\rho_0\left(1+\frac{\rho_0 g y}{B}\right)\)

Question 5. Two identical cylindrical containers contain a liquid of density d. The bases of the containers lie on the same horizontal plane. The depths of liquid in the two containers are h₁ and h₂ respectively and the base areas of both containers is A. If the two containers are connected by a pipe, then the work done by gravity to equalize the levels of liquid in the two containers is

1. (h₁ – h₂)gd
2. (h₁-h₂)gAd
3. \(\frac{1}{2}\left(h_1-h_2\right)^2 g A d\)
4. \(\frac{1}{4}\left(h_1-h_2\right)^2 g A d\)

Answer: 4. \(\frac{1}{4}\left(h_1-h_2\right)^2 g A d\)

Question 6. The dimensions of a block of iron of density 5 g · cm^-3 are 5 cm x 5 cm x 5 cm. It is weighed by immersing it completely in water. Its apparent weight will be

1. (5x5x5x5)xg
2. (4x4x4x5)xg
3. (3x5x5x5)xg
4. (4x5x5x5)xg

Answer: 2. (5x5x5x5)xg

Question 7. There is a layer of oil over mercury in a container. The density of mercury is 13.6 g • cm^-3 and that of the oil is 0. 8 g-cm^-3. A homogeneous sphere remains immersed with half of its volume in mercury and the other half in oil. The density of the material of the sphere in g • cm^-3 is

1. 3.3
2. 6.4
3. 7.2
4. 12.8

Answer: 3. 7.2

Question 8. When a block is suspended in air from a spring balance, it reads 60 N. When the block is immersed completely in water, the spring balance reads 40 N. The specific gravity of the block is

1. 3/2
2. 6
3. 2
4. 3

Answer: 4. 3

Question 9. A wooden cubic block with a 200 g mass floats in water just fully immersed. When the mass is removed, the block floats up by 2 cm. The length of each side of the cube is

1. 5 cm
2. 10 cm
3. 15 cm
4. 20 cm

Answer: 2. 10 cm

Question 10. A piece of ice of density 900 kg · m^-3 floats on water. The part of the piece of ice that remains outside the water surface is

1. 20%
2. 35%
3. 10%
4. 25%

Answer: 3. 10%

Question 11. Two stretched membranes of area 2m² and 3m² are kept at the same depth in a liquid. The ratio of the pressures on them is

1. 1:1
2. 2:3
3. √2:√3
4. 2²:3²

Answer: 1. 1: 1

Question 12. Two containers A and B of different shapes, but having the same base area are filled with water up to the same height h. The effective force on the base of the container A is F_A and that on the base of container B is F_B. If the weights of the two containers are W_A and W_B respectively, then which of the following is correct?

1. F_A>F_B’ W_A> W_B
2. F_A = F_B: W_A> W_B
3. F_A = F_B‘; W_A<W_B
4. F_A = F_B‘ ; W_A<W_B

Answer: 2.

Question 13. If a pressure is applied on any part of an enclosed fluid, then that pressure

1. Acts on all parts of the fluid with increased magnitude
2. Acts on the wall of the container with decreased magnitude
3. Increases according to the mass of the fluid and is then transmitted
4. Is transmitted throughout the fluid with undiminished magnitude and acts normally on tire wall of the container in contact with the fluid

Answer: 4. Is transmitted throughout the fluid with undiminished magnitude and acts normally on tire wall of the container in contact with the fluid

Question 14. The pressure exerted by a liquid at the bottom of the container containing the liquid does not depend on

1. Acceleration due to gravity
2. Height of the liquid column in the container
3. Area of the bottom of the container
4. Density of the liquid

Answer: 3. Area of the bottom of the container

Question 15. Bar is a unit of pressure. 1 bar = ?

1. 10⁴ Pa
2. 10⁵ Pa
3. 10⁶ Pa
4. 10⁷ Pa

Answer: 2. 10⁵ Pa

Question 16. The working principle of a hydraulic press depends on

1. Boyle’s law
2. Pascal’s law
3. Dalton’s law of partial pressure
4. Newton’s law of gravitation

Answer: 2. Pascal’s law

Question 17. A thin uniform cylindrical shell, closed at both ends is partially filled with water. It is floating vertically in water in a half-submerged state. If pc is the relative density of the material of the shell with respect to water, then the correct statement is that the shell is

1. More than half filled if ρ_c is less than 0.5
2. More than half filled if ρ_c is less titan 1.0
3. Half filled if ρ_c is less than 0.5
4. Less than half filled if ρ_c is less than 0.5

Answer: 4. Less than half filled if ρ_c is less than 0.5

Question 18. Which of the following works on Pascal’s law?

1. Barometer
2. Hydraulic lift
3. Venturi meter
4. Sprayer

Answer: 2. Hydraulic lift

Question 19. If the liquid used in a hydraulic press is replaced by a gas, then the press

1. Continues to work as before
2. Does not work
3. Works but cannot be used for heavy duty
4. None of the above

Answer: 3. Works but cannot be used for heavy-duty

Question 20. The radii of two thin circular discs are 0.03 m and 0.04 m respectively. They are placed inside a liquid at the same depth. The ratio of the thrusts acting on them is

1. 9: 16
2. 3:4
3. 4:3
4. √3:2

Answer: 1. 9: 16

Question 21. A given shaped glass tube having uniform cross section is filled with water and is mounted on a rotable shaft as shown in Fig. If the tube is rotated with a constant angular velocity ω, then

1. Water level 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 goes up
4. Water level remain same in both sections

Answer: 1. Water level in both sections A and B go up

Question 22. The diameters of the smaller and larger pistons of a hydraulic press are d₁ and d₂ respectively. If the force applied on the smaller piston is F₁, then the force developed on the larger piston will be

1. \(F_2=\frac{d_2^2}{d_1^2} \cdot F_1\)
2. \(F_2=\frac{d_1^2}{d_2^2}, F_1\)
3. \(F_2=\frac{d_1^2}{d_2^2} \cdot \frac{1}{F_1}\)
4. \(F_2=\frac{d_2^2}{d_1^2} \cdot \frac{1}{F_1}\)

Answer: 1. \(F_2=\frac{d_2^2}{d_1^2} \cdot F_1\)

Question 23. A hole is made at a depth h on the wall of a container containing a liquid. The velocity of efflux of the liquid through the hole is

1. Zero
2. √gh
3. √2gh
4. Dependent on the density of the liquid

Answer: 3. √2gh

Question 24. A cylindrical vessel contains water up to a height of H. A hole is made in the wall of the vessel. If the jet of water coming out from the hole traverses the maximum distance from the base of the vessel, then the hole is situated

1. At a depth H from the upper surface of water
2. At a depth H/2 from the upper surface of water
3. At a depth H/4 from the upper surface of water
4. At a depth 3H/4 from the upper surface of water

Answer: 2. At a depth H/2 from the upper surface of water

Question 25. A tank contains water up to a height H. A hole is made at a depth h from the upper surface. The horizontal range of the jet of water coming out from the hole is

1. \(2 \sqrt{h(H-h)}\)
2. \(4 \sqrt{h(H+h)}\)
3. \(4 \sqrt{h(H-h)}\)
4. \(2 \sqrt{h(H+h)}\)

Answer: 1. \(2 \sqrt{h(H-h)}\)

Question 26. Of the following substances, which one can be lifted upwards with more ease with the help of a hydrogen-filled balloon?

1. 1 kg steel
2. 1 kg feather
3. 1 kg lead
4. 1 kg water

Answer: 2. 1 kg feather

Question 27. There is a coin placed on a wooden block floating on water as shown in Fig. In this figure, l and h are directed. After sometime, the coin falls into the water. Then it is observed that

1. l decreases but h increases
2. l increases but h decreases
3. Both l and h increase
4. Both l and h decrease

Answer: 4. Both l and h decrease

Question 28. A man is carrying a bucket of water in one hand and a piece of plastic in the other. When the piece of plastic is dropped into the water of the bucket, then the man

1. Carries more weight than before
2. Carries less weight than before
3. Carries the same wei|ht as before
4. Carries more or less weight than before depending on the density of the plastic

Answer: 3. Carries the same wei|ht as before

Question 29. A body remains floating in a liquid kept in a beaker. If the entire system falls under gravity, then the upthrust of the liquid acting on the body will be

1. Zero
2. Equal to the weight of the displaced liquid
3. Equal to the weight of the part of the body exposed to air
4. Equal to the weight of the immersed part of the body in that liquid

Answer: 1. Zero

Question 30. Figure is here shows the vertical cross-section of a vessel filled with a liquid of density ρ. The normal thrust per unit area on the walls of the vessel at point P, as shown will be

1. hρg
2. Hρg
3. (H-h)pg
4. (H- h)ρgcosθ

Answer: 3. (H-h)pg

Question 31. A body floats in a liquid fully submerged. If the body is pressed slightly downwards and then released, it will

1. Oscillate up and down
2. Remain at rest in its new position
3. Return to the previous position quickly
4. Return to the previous position slowly

Answer: 2. Remain at rest in its new position

Question 32. A bird is sitting on the floor of a wire cage. This cage is carried by a boy. In this situation, if the bird starts flying inside the cage, then the boy will feel that

1. The cage has become heavier than before
2. The cage has become fighter than before
3. The weight of the cage remains the same as before
4. The cage appears fighter first and then heavier

Answer: 2. The cage has become fighter than before

Question 33. A boat of length 3 m and breadth 2 m is floating on water in a lake. When a man rides on the boat, it sinks 1 cm more. The mass of the man is

1. 60 kg
2. 72 kg
3. 12 kg
4. 128 kg

Answer: 1. 60 kg

Question 34. A wooden block is floating on water in a closed vessel. If the entire space above the water is evacuated, then

1. The block floats up more
2. The block sinks more
3. The block will remain in the same position
4. None of the above

Answer: 2. The block sinks more

Question 35. A body is floating on a liquid. The upthrust by the liquid acting on the body is

1. Equal to the weight of the displaced liquid
2. Zero
3. Less than the weight of the displaced liquid
4. Weight of the body – weight of the displaced liquid

Answer: 1. Equal to the weight of the displaced liquid

Question 36. A block of wood and a solid lead sphere are kept in a container with water up to its brim. Now, if the lead sphere is placed on the floating block of wood, then the level of water

1. Will remain the same
2. Will fall
3. Will rise and some water will overflow from the container
4. Will change depending on the shape of the lead sphere

Answer: 3. Will rise and some water will overflow from the container

Question 37. Two solid pieces one of steel and other of aluminium when immersed completely in water have equal weights. When the solid pieces are weighed in air

1. The weight of aluminium is half the weight of steel
2. Steel piece will weigh more
3. They have the same weight
4. Aluminium piece will weigh more

Answer: 4. Aluminium piece will weigh more

Question 38. A man is sitting on a boat in a pond. If the man drinks some water from the pond, the level of water in the pond

1. Will remain the same
2. Will fall
3. Will rise
4. Will rise or fall depending on the amount of water drunk by the man

Answer: 1. Will remain the same

Question 39. A piece of ice is floating on a liquid of density 1.5 g- cm^-3 kept in a beaker. If the piece of ice melts completely, then the liquid level in the beaker

1. Will rise
2. Will fall
3. Will remain the same
4. Will fall down first and then return to the original level

Answer: 1. Will rise

Question 40. A wooden block of mass 120 kg floats on water. The density of the wooden block is 600 kg • m^-3. The weight that should be placed on the wooden block so that it just sinks will be

1. 80 kg
2. 50 kg
3. 60 kg
4. 30 kg

Answer: 1. 80 kg

Question 41. A body with a uniform cross-section floats on a liquid. The density of the liquid is thrice the density of the body. The part of the body that remains above the liquid is

1. 2/3
2. 5/6
3. 1/6
4. 1/3

Answer: 1. 2/3

Question 42. A body remains floating in a liquid with a part of it immersed in the liquid. If the body along with the liquid is taken to the moon, then the body

1. Will remain floating as before
2. Will remain floating with a greater part of it inside the liquid than before
3. Will remain floating with a lesser part of it inside the liquid than before
4. Will sink in the liquid

Answer: 1. Will remain floating as before

Question 43. With increase in temperature, the upthrust acting on a body immersed in a liquid

1. Increases
2. Decreases
3. Remains unchanged
4. None of these

Answer: 2. Decreases

Question 44. A block of wood of mass m and density ρ is tied with a thread and rigidly fixed at the bottom of a vessel. The vessel is filled with a liquid of density σ(σ > ρ). The tension acting on the string is

1. \(\left(\frac{\sigma-\rho}{\sigma}\right) m g\)
2. \(\left(\frac{\sigma-\rho}{\rho}\right) m g\)
3. \(\frac{\rho}{\sigma} m g\)
4. \(\frac{\sigma}{\rho} m g\)

Answer: 2. \(\left(\frac{\sigma-\rho}{\rho}\right) m g\)

In this type of questions more than one options are correct.

Question 45. A spring balance A reads 2 kg with a block suspended from it. Another balance B reads 5 kg when a beaker with liquid is put on the pan of the balance. When the block is immersed in water

1. The balance a will read more than 2 kg
2. The balance b will read more than 5 kg
3. The balance a will read less than 2 kg
4. The balance a will read 2 kg and the balance b will read 5 kg

Answer:

2. The balance b will read more than 5 kg

3. The balance a will read less than 2 kg

Question 46. A closed vessel is half filled with water. There is a hole near the top of the vessel and air is pumped out from this hole. As a result

1. The water level will rise up in the vessel
2. The pressure at the surface of the water will decrease
3. The force by the water on the bottom of the vessel will decrease
4. The density of the liquid will decrease

Answer:

2. The pressure at the surface of the water will decrease

3. The force by the water on the bottom of the vessel will decrease

Question 47. When a body of density ρ and volume V is floating in a liquid of density σ

1. Its true weight is vρg
2. Loss in its weight is vσg
3. Its apparent weight is zero
4. Its density ρ is less than that of liquid σ

Answer:

1. Its true weight is vρg

3. Its apparent weight is zero

4. Its density p is less than that of liquid σ

Question 48. Two liquids that do not react chemically are placed in a bent tube as shown in Fig. Which of the following statements are correct?

1. The pressure at the interface must be same, calculated via both tubes
2. The heights of the liquids above their surfaces of separation are inversely proportional to their densities
3. Both 1 and 2
4. Neither 1 nor 2

Answer:

1. The pressure at the interface must be same, calculated via both tubes
2. The heights of the liquids above their surfaces of separation are inversely proportional to their densities
3. Both 1 and 2

Question 49. A wire is found to have a length L when it is loaded with a block of mass M and relative density n. When the block is immersed in water, the length of the wire reduces by x, then

1. Weight of water displaced when the block is immersed in water is mg/ n
2. The apparent loss of weight due to immersion is \(m g\left(1-\frac{1}{n}\right)\)
3. The original length of the wire before it was loaded is L₁ = L -nx
4. The original length of the wire before it was loaded is L₁ =L- x/n

Answer:

1. Weight of water displaced when the block is immersed in water is mg/ n
2. The apparent loss of weight due to immersion is \(m g\left(1-\frac{1}{n}\right)\)
3. The original length of the wire before it was loaded is L₁ = L -nx

Question 50. A uniform cylinder of density ρ and cross-sectional area A floats in equilibrium in two non-mixing liquids of densities ρ₁ and ρ₂ as shown in Fig. The length of the part of the cylinder in air is h and the lengths of the part of the cylinder immersed in the liquid are h₁ and h₂ as shown in the figure. Which among the following are correct?

1. The net resultant force acting on the cylinder by the liquid of density ρ₁ is zero
2. h = \(h_1\left(\frac{\rho_1}{\rho}-1\right)+h_2\left(\frac{\rho_2}{\rho}-1\right)\)
3. The cylinder is depressed in such a way that its top surface is just covered by the liquid of density ρ₁ and then released. The restoring force acting on the cylinder is f = hAρ₂g
4. In choice 3 above, the acceleration of the cylinder is a = \(a=\frac{h+\rho_2 g}{\left(h+h_1+h_2\right) \rho}\)

Answer: All are correct

Question 51. Two solid spheres A and B of equal volumes but of different. densities d_A and d_B are connected by string. They are fully immersed in a fluid of density d_F. They get arranged into an equilibrium state as shown in Fig. with a tension in the string. The arrangement is possible only if

1. d_A< d_F
2. d_B > d_F
3. d_A >d_F
4. d_A+d_B = 2d_F

Answer:

1. dA< dp

2. dB> dp

4. dA+dB = 2dF