Measurements in Physics (DP IB Physics: HL): Exam Questions

Derive the units of pressure in terms of fundamental SI units.

At sea level, the pressure due to the atmosphere is 101 kPa. In the Mariana Trench, at the bottom of the Pacific Ocean, the pressure is around 110 MPa.

Determine how many orders of magnitude greater the pressure at the bottom of the Mariana Trench is than the pressure at sea level.

An electron microscope is used to analyse the arrangement of atoms and their nuclei in a new design for a special sheet of silver foil. The foil is a new material being added to various components in a military medical aircraft. 

The sheet of silver foil has a thickness of 0.992 µm. A silver atom has a radius of 165 pm. 

Estimate the number of layers of atoms in a sheet of silver foil.

The barn (b) is a derived unit used to describe the cross-sectional area of a nucleus. 1 b is equivalent to 100 fm².

Calculate the value of 1 nb in m².

Einstein’s famous equation Energy (J) = Mass (kg) × (Speed of light (m s^–1))²­ demonstrates that energy and matter are interchangeable.

Atomic mass unit, 1 u = 931.5 MeV

1 eV = 1.60 × 10^–19 J

Use this equation to show that the value in kg of 1 u of silver in the foil is approximately equal to the mass of a proton in kg.  

X–ray pulsars are detected by X–ray telescopes on a satellite in low Earth orbit 2000 km above the surface of the Earth. 

Calculate the number of cubic millimetres (mm³) in a volume of 2000 km³.

X–rays from a pulsar travel at the speed of light and are detected on Earth with a wavelength of 8.0 nm. 

Calculate the frequency of the X–rays in PHz. Give your answer to an appropriate number of significant figures. . 

X–rays from the nearest pulsar PSR J0109–1431 take 8.82 Gs to travel to Earth. 

Calculate the number of oscillations of the X–rays from the pulsar to the surface of the Earth. Give your answer to an appropriate number of significant figures.

Show the distance from Earth to PSR J0109–1431 is around 280 light years.

A student conducts an experiment to study the variation of resistance R of a negative temperature coefficient (NCT) thermistor with temperature T. The data from the experiment is shown plotted on the graph.

The electric current through the thermistor for T = 283 K is 0.0078 mA. 

What is the units of resistance R in SI units?

Convert 0.0078 mA to A and write in standard form.

Calculate the ratio  when T = 291 K. Write your answer in fundamental SI units to an appropriate number of significant figures.

Estimate the resistance of the thermistor at a temperature of 335 K

A simple pendulum oscillates in simple harmonic motion. It can be assumed that there are no energy losses in the system.

Prove dimensionally that the work-energy principle applies for this system.

Complete the following table by giving the SI base units. Then estimate the order of magnitude for each of the physical quantities.

The density, ρ, and pressure, p, of a gas are related by the expression:

where x and γ are constants.

Given that the constant γ is dimensionless 

(i) Determine the unit of x.

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(ii) Suggest what quantity is being represented by the symbol x.

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Identify the quantity with the SI base units of m³ kg⁻¹ s⁻².

Convert the following measurements to the appropriate unit, and express to an appropriate number of significant figures.   

90 000 GW = ____________ mW

45.1 hF = _____________ fF

0.60 pm = _____________ km

214 minutes = _____________ ms

A sheet of silver has a thickness of 0.671 µm. A silver atom has a radius of 172 pm.

Estimate the number of layers of atoms in this sheet to the nearest thousand.

Identify the variable that has the SI base units kg m² s⁻³ A⁻².

Explain why potential difference is not defined as current × resistance.

Convert 0.01 kWh into PeV.

Tensile stress (σ) is defined as the force applied per unit cross-sectional area on a material. The tensile strength is the maximum amount of tensile stress a material can be subjected to before fracturing, meaning that it is equivalent to the tensile stress at the breaking point.

The humerus bone is approximately cylindrical and has a tensile strength of 0.17 GPa and a diameter of 20 mm. 

Calculate the maximum force on the humerus bone before it fractures.

The femur bone is the strongest bone in the body. It has a tensile strength of 0.135 kN mm^–2. 

Calculate the tensile strength of the femur bone in GPa.

Calculate the number of cubic millimetres (mm³) in 23 km³.

Estimate the time it takes light to cross the nucleus of a hydrogen atom.

Estimate the order of magnitude with an appropriate SI unit and correct prefix for the following quantities.

(i)   Mass of an aeroplane.

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(ii)   Current through an LED.

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(iii)   Time between two heartbeats.

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1 u is the atomic mass unit and a common unit used in nuclear physics.

Show that its value in kg is approximately equal to the mass of a proton in kg.

The cross-sectional area of nuclei are commonly measured in the units barn, which are represented by the symbol b. 1 barn = 100 fm²

Calculate the value of a nano barn (nb) in m².