Density & Pressure (Cambridge (CIE) A Level Physics)

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.

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?

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 ?

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 ?

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

What is the depth x of the oil ?

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

The density of mercury is 13 600 kg m^–3

Which pair of values of h₁ and h₂ is possible? 

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 ?

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

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   ?

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 ?

A U-tube closed a tone 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

What is the height of the mercury column?

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?

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 ?

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 p_t and p_b at its top and bottom surfaces respectively.

Which expression is equal to the upthrust on the block ?

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 ?

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.

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  ? 

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.

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 ?

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

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 ?

Two solid substances P and Q have atoms of mass M_P and M_Q 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 ?

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 ?

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?

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

The density of seawater is 1020 kg m⁻³

What fraction of the ice is submerged underwater ?