SI Units (Cambridge (CIE) A Level Physics): Exam Questions

The average kinetic energy E of a gas molecule is given by the equation

$E=\frac{3}{2}kT$

where T is the thermodynamic (kelvin) temperature.

What are the SI base units of k?

The units of all physical quantities can be expressed in terms of SI base units.

Which pair contains quantities with the same base units?

The table contains some quantities, together with their symbols and units.

Which expression has the units of energy?

What is the ratio $\frac{{10}^{-3}\mathrm{THz}}{{10}^3\mathrm{kHz}}$ ?

Which of the following correctly expresses the volt in terms of SI base units?

The equation relating pressure and density is $P=\rho gh$

How can both sides of this equation be written in terms of base units?

What is the ratio $\frac{{10}^2\text{ THz}}{{10}^{-4}\text{ pHz}}$ ?

The speed v of a liquid leaving a tube depends on the change in pressure ΔP and the density ρ of the liquid. The speed is given by the equation

$v=k{\left(\frac{∆P}{\rho }\right)}^n$

where k is a constant that has no units.

What is the value of n?

The frictional force F on a sphere falling through a fluid is given by the formula

$F=6\mathrm{\pi }r\eta v$

where r is the radius of the sphere, η is a constant relating to the fluid and v is the velocity of the sphere.

What are the units of η ?

When a constant braking force is applied to a vehicle moving at speed v, the distance d moved by the vehicle as it comes to rest is given by the expression

$d=k{v}^2$

where k is a constant.

When d is measured in metres and v is measured in metres per second, the constant has a value of k₁.

What is the value of the constant k when the distance is measured in metres, and the speed is measured in kilometres per hour?

The drag coefficient C_d is a number with no units. It is used to compare the drag on different cars at different speeds. It is given by the equation

$C_d=\frac{2F}{\rho v^{n}A}$

where F is the drag force on the car, ρ is the density of the air, A is the cross-sectional area of the car and v is the speed of the car. 

What is the value of n?

Which formula could be correct for the speed v of ocean waves in terms of the density ρ of sea-water, the acceleration of free fall g, the height h of the wave and the wavelength λ?

The equation for the terminal velocity of a sphere of radius r falling under acceleration due to gravity, g, through a liquid with density ⍴ and viscosity ɳ, measured in kg m⁻¹ s⁻¹ is:

$v_t=\frac{2}{9}\frac{g{r}^n\rho }{\eta }$

What is the value of n?

The current $I$ through a semiconductor diode is given by:

$I=I_0{e}^{\frac{-qV}{nT}}$

where $I_0$ is the initial current, $q$ is the charge of an electron, $V$ is the applied potential difference, $T$ is the temperature, and $n$ is a constant.

What is the unit of $n$ when expressed in SI base units?