A LevelPhysicsCIEExam Questions4. Forces, Density & Pressure4.2 Forces: Density & Pressure

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Forces: Density & Pressure (CIE A Level Physics)

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4.2 Forces: Density & Pressure

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4.2 Forces: Density & Pressure

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11 mark

The formula for hydrostatic pressure is P equals p g h

 Which equation, or principle of physics, is used in the derivation of this formula?

  • density = mass ÷ volume

  • potential energy = mgh

  • atmospheric pressure decreases with height

  • density increases with depth

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21 mark

The density of mercury is 13.6 × 103 kg m–3

 The pressure difference between the bottom and the top of a column of mercury is 100 kPa.

 What is the height of the column?

  • 0.75 m

  • 1.3 m

  • 7.4 m

  • 72 m

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31 mark

An object, immersed in a liquid in a tank, experiences an upthrust.

 What is the physical reason for this upthrust?

  • the density of the body differs from that of the liquid

  • the density of the liquid increases with depth

  • the pressure in the liquid increases with depth

  • the value of g in the liquid increases with depth

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41 mark

The Mariana Trench in the Pacific Ocean has a depth of about 10 km.

 Assuming that sea water is incompressible and has a density of about 1020 kg m–3, what would be the approximate pressure at that depth ?

  • 105 Pa

  • 106 Pa

  • 107 Pa

  • 108 Pa

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51 mark

The diagram represents a sphere under water. P, Q, R and S are forces acting on the sphere, due to the pressure of the water.

cie-ial-physics-images-4-2-m-q5

Each force acts perpendicularly to the sphere’s surface. P and R act in opposite directions vertically. Q and S act in opposite directions horizontally.

 Which information about the magnitudes of the forces is correct ?

  • P < R and S = Q

  • P > R and S = Q

  • P = R and S = Q and P ≠ S

  • P = R and S = Q and P = S

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61 mark

Water in a bath varies in depth from 20.0 cm at the shallow end to 30.0 cm at the end with the plug.

cie-ial-physics-images-4-2--e-q6

The density of the water is 1000 kg m–3

 What is the pressure of the water acting on the plug ?

  • 0.98 kPa

  • 2.0 kPa

  • 2.9 kPa

  • 290 kPa

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71 mark

A submarine is in equilibrium in a fully submerged position.

cie-ial-physics-images-4-2--e-q7

What causes the upthrust on the submarine?

  • the air in the submarine is less dense than sea water

  • the sea water exerts a greater upward force on the submarine than the weight of the steel

  • the submarine displaces its own volume of sea water

  • there is a difference in water pressure acting on the top and on the bottom of the submarine

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81 mark

The diagram shows a rectangular block of mass 8.2 kg immersed in sea water of density 1.10 × 103 kg m–3

cie-ial-physics-images-4-2--e-q8

What is the difference in pressure between the top and bottom surfaces of the block?

  • 2.2 × 102 Pa

  • 2.2 × 103 Pa

  • 1.8 × 104 Pa

  • 2.3 × 104 Pa

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91 mark

A horizontal plate of area 0.036 m2 is beneath the surface of a liquid of density 

930 kg m–3. The force on the plate due to the pressure of the liquid is 290 N.

 What is the depth of the plate beneath the surface of the liquid?

  • 0.88 m

  • 1.13 m

  • 8.7 m

  • 9.1 m

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101 mark

A rectangular metal bar exerts a pressure of 15 200 Pa on the horizontal surface on which it rests.

 If the height of the metal bar is 80 cm, what is the density of the metal ?

  • 19 kg m–3 

  • 190 kg m–3

  • 1900 kg m–3

  • 19 000 kg m–3

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11 mark

Four cuboids with identical length, breadth and height are immersed in water. The cuboids are held at the same depth and in identical orientations by vertical rods, as shown.

cie-ial-physics-images-4-2--m-q1

Water has density ρ

Cuboid W is made of material of density 4ρ

Cuboid X is made of material of density 2ρ

Cuboid Y is made of material of density ρ

Cuboid Z is made of material of density ½ ρ

 Which statement is correct?

  • the upthrust of the water on each of the cuboids is the same

  • the upthrust of the water on W is twice the upthrust of the water on X

  • the upthrust of the water on Z is twice the upthrust of the water on Y

  • the upthrust of the water on Y is zero

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21 mark

Atmospheric pressure at sea level has a value of 100 kPa.

 The density of sea water is 1020 kg m–3

 At which depth in the sea would the total pressure be 150 kPa ?

  • 5 m

  • 25 m

  • 50 m

  • 55 m

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31 mark

A beam of α-particles collides with a lead sheet. Each α-particle in the beam has a mass of 6.6 × 10–27 kg and a speed of 1.5 × 107 m s–1

 5.0 × 104 α-particles per second collide with an area of 1.0 cm2 of lead. Almost all of the α-particles are absorbed by the lead so that they have zero speed after collision.

 What is an estimate of the average pressure exerted on the lead by the α-particles ?

  • 5.0 × 10–15 Pa

  • 5.0 × 10–13 Pa

  • 5.0 × 10–11 Pa

  • 5.0 × 10–9 Pa

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41 mark

A bore-hole of depth 2000 m contains both oil and water as shown. The pressure due to the liquids at the bottom of the bore-hole is 17.5 MPa. The density of the oil is 830 kg m–3 and the density of the water is 1000 kg m–3

cie-ial-physics-images-4-2--m--q4

What is the depth x of the oil ?

  • 907 m

  • 1000 m

  • 1090 m

  • 1270 m

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51 mark

Two bulbs X and Y containing air at different pressures are connected by a tube P which contains two mercury threads.

cie-ial-physics-images-4-2--m--q5

The density of mercury is 13 600 kg m–3

 Which pair of values of h1 and h2 is possible? 

 

h1 / cm

h2 / cm

A

B

C

D

4.0

6.0

12.0

18.0

2.0

6.0

18.0

12.0

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    61 mark

    1.5 m3 of water is mixed with 0.50 m3 of alcohol. The density of water is 1000 kg m–3 and the density of alcohol is 800 kg m–3

     What is the density of the mixture with volume 2.0 m3 ?

    • 850 kg m–3 

    • 900 kg m–3

    • 940 kg m–3

    • 950 kg m–3

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    71 mark

    The diagram shows two vessels, P and Q, both with sides inclined at 45°

    cie-ial-physics-images-4-2--m--q7

    Vessel P tapers outwards and vessel Q tapers inwards, as shown.

     Both vessels contain a liquid. The depth of the liquid in the vessels is the same. The liquid in vessel P is twice as dense as the liquid in vessel Q.

     What is the ratio fraction numerator p r e s s u r e space d u e space t o space t h e space l i q u i d space o n space t h e space b a s e space o f space P over denominator p r e s s u r e space d u e space t o space t h e space l i q u i d space o n space t h e space b a s e space o f space Q end fraction  ?

    • 2 over 1

    • fraction numerator square root of 2 over denominator 1 end fraction

    • fraction numerator 1 over denominator square root of 2 end fraction

    • 1 half

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    81 mark

    At a depth of 20 cm in a liquid of density 1800 kg m–3, the pressure due to the liquid is p.

     Another liquid has a density of 1200 kg m–3

     What is the pressure due to this liquid at a depth of 60 cm ?

    • p over 2

    • fraction numerator 3 p over denominator 2 end fraction

    • 2 p

    • 3 p

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    91 mark

    A U-tube closed at one end contains mercury. Air at a pressure of 5.0 × 104 Pa is trapped at the closed end. The other end is open to the atmosphere and is fitted with a piston of mass 5.0 kg and cross-sectional area 5.0 × 10–4 m2

     The density of mercury is 13 600 kg m–3 and atmospheric pressure is 1.01 × 105 Pa

    cie-ial-physics-images-4-2--m--q9

    What is the height of the mercury column?

    • 37 cm

    • 44 cm

    • 74 cm

    • 110 cm

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    101 mark

    A ball is falling at terminal speed in still air. The forces acting on the ball are upthrust, viscous drag and weight.

     What is the order of increasing magnitude of these three forces?

    • upthrust → viscous drag → weight

    • viscous drag → upthrust → weight

    • viscous drag → weight → upthrust

    • weight → upthrust → viscous drag

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    11 mark

    The density of water is 1.0 g cm–3 and the density of glycerine is 1.3 g cm–3

     Water is added to a measuring cylinder containing 40 cm3 of glycerine so that the density of the mixture is 1.1 g cm–3. Assume that the mixing process does not change the total volume of the liquid

     What is the volume of water added ?

    • 40 cm3

    • 44 cm3

    • 52 cm3

    • 80 cm3

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    21 mark

    A cylindrical block of wood has cross-sectional area A and weight W. It is totally immersed in water with its axis vertical. The block experiences pressures pt and pb at its top and bottom surfaces respectively.

     Which expression is equal to the upthrust on the block ?

    • open parentheses p subscript b minus p subscript t close parentheses A plus W

    • open parentheses p subscript b minus p subscript t close parentheses

    • open parentheses p subscript b minus p subscript t close parentheses A

    • open parentheses p subscript b minus p subscript t close parentheses A minus W

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    31 mark

    Full-fat milk is made up of fat-free milk mixed with fat.

     A volume of 1.000 × 10–3 m3 of full-fat milk has a mass of 1.035 kg. It contains 4.00% fat by volume.

     The density of fat-free milk is 1.040 × 103 kg m–3

     What is the density of fat ?

    • 1.25 × 102 kg m–3

    • 9.15 × 102 kg m–3

    • 9.28 × 102 kg m–3

    • 1.16 × 103 kg m–3

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    41 mark

    A W-shaped tube contains two amounts of mercury, each open to the atmosphere. Air at pressure P is trapped in between them. The diagram shows two vertical distances x and y.

    cie-ial-physics-images-4-2--h--q4

    Atmospheric pressure is equal to the pressure that would be exerted by a column of mercury of height 760 mm. The pressure P is expressed in this way.

     Which values of x, y and P are possible  ? 

     

    x / mm

    y / mm

    P / mm of

    Mercury

    A

    B

    C

    D

    20

    20

    30

    30

    20

    30

    20

    30

    780

    780

    810

    790

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      51 mark

      The diagram shows a metal cube of density ρ suspended from a spring balance before and during immersion in water. Each face of the cube has a surface area A and each edge has length h.

      cie-ial-physics-images-4-2--h--q5

      A reduction in the balance reading occurs as a consequence of the immersion. The cube experiences pressures p1 and p2 at its top and bottom surfaces respectively.

       What is the value of the upthrust on the metal cube during immersion ?

      • A h rho g

      • A h rho g plus p subscript 1 A

      • p subscript 2 A

      • p subscript 2 A minus p subscript 1 A

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      61 mark

      The diagram shows a flask connected to a U-tube containing liquid. The flask contains air at atmospheric pressure.

      cie-ial-physics-images-4-2--h--q6

      The flask is now gently heated and the liquid level in the right-hand side of the U-tube rises through a distance h. The density of the liquid is ρ.

       What is the increase in pressure of the heated air in the flask ?

      • h rho

      • 1 half h rho g

      • h rho g

      • 2 h rho g

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      71 mark

      Two solid substances P and Q have atoms of mass MP and MQ respectively. They have n P and n Q atoms per unit volume.

       The density of P is greater than the density of Q.

       Which expression must be correct ?

      • M subscript P greater than space M subscript Q

      • n subscript P space greater than space n subscript Q

      • M subscript colon P end subscript n subscript P space greater than space M subscript Q n subscript Q

      • M subscript P over n subscript P space greater than space M subscript Q over n subscript Q

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      81 mark

      Liquid Q has twice the density of liquid R.

       At depth x in liquid R, the pressure due to the liquid is 4 kPa.

       At what depth in liquid Q is the pressure due to the liquid 7 kPa ?

      • fraction numerator 2 x over denominator 7 end fraction

      • fraction numerator 7 x over denominator 8 end fraction

      • fraction numerator 8 x over denominator 7 end fraction

      • fraction numerator 7 x over denominator 2 end fraction

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      91 mark

      A child drinks a liquid of density ρ through a vertical straw.

       Atmospheric pressure is p0 and the child is capable of lowering the pressure at the top of the straw by 10%. The acceleration of free fall is g.

       What is the maximum length of straw that would enable the child to drink the liquid?

      • fraction numerator p subscript 0 over denominator 10 rho g end fraction

      • fraction numerator 9 p subscript 0 over denominator 10 rho g end fraction

      • fraction numerator p subscript 0 over denominator rho g end fraction

      • fraction numerator 10 p subscript 0 over denominator rho g end fraction

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      101 mark

      Icebergs typically float with a large volume of ice beneath the water. Ice has a density of 917 kg m–3.

       The density of seawater is 1020 kg m−3

       What fraction of the ice is submerged underwater ?

      • 0.05 space V subscript i

      • 0.10 space V subscript i

      • 0.90 space V subscript i

      • 0.95 space V subscript i

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