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.

The density and pressure of a gas are related by the expression

where is a dimensionless constant.

(i) Determine the unit of in terms of fundamental SI units.

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(ii) Suggest the physical quantity represented by .

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

Estimate the order of magnitude and give an appropriate SI unit for:

(i) the mass of an aeroplane

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(ii) the current through an LED

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(iii) the time between two heartbeats.

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Determine the value of 0.01 kW h in PeV.

Tensile stress 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 that can be applied to 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.

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

Explain why potential difference is not defined as the product of current and resistance.

The force of gravitational attraction between two objects with masses and separated by a distance is given by

where is the universal gravitational constant.

Show that the fundamental SI units of are m³ kg⁻¹ s⁻².

For a planet of mass and radius , the escape velocity from the planet's surface is given by

Show that this formula is dimensionally consistent.

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 172 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.

The cross-sectional area of a silver nucleus is approximately equal to 1 b. 1 b is equivalent to 100 fm².

Determine how many orders of magnitude greater the cross-sectional area of a silver atom is than the cross-sectional area of a silver nucleus.

Einstein's equation describes the interchangeable nature of energy and matter, and is given by

where is energy, is mass, and is the speed of light.

The mass of a silver atom is 107.87 u.

Show that the mass of silver in 1 cm² of foil is equivalent to an energy of 4 × 10¹⁰ J.

X–rays emitted by a pulsar travel at the speed of light and are detected on Earth with a wavelength of 3.5 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 J0108-1431, take 13.4 Gs to travel to Earth. 

Calculate the number of oscillations completed by the X–rays as they travel from the pulsar to the Earth. Give your answer to an appropriate number of significant figures.

Show that the distance from Earth to PSR J0108-1431 is around 420 light-years.

An experiment is undertaken to investigate the relationship between the temperature and the resistance of a negative temperature coefficient (NTC) thermistor.

The graph shows the variation of with temperature .

Draw the line of best-fit for the data.

(i) Determine the gradient of the line when = 291 K.

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(ii) State an appropriate unit for your answer to (b)(i).

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Use your graph to estimate the resistance of the thermistor when = 335 K.

It is suggested that the variation with of the resistance is of the form

where and are constants.

State how the value of may be determined from a suitable graph.