Dimensional Analysis Quiz 5 | Physics

See if you can determine the dimensions of " $k$ " in each of the following (where $x$ is a distance, $R$ is a radius, $h$ is Planck's constant with SI units of joules x second, $f$ is frequency and $T$ is absolute temperature):

$sin (kx)$
$10^{kx}$
$cot (kx^2/R)$
$e^{hf/kT}-1$

Check your answers

dimensions of $k = L^{-1}$
dimensions of $k = L^{-1}$
dimensions of $k = L^{-1}$
dimensions of $k = M\cdot L^2\cdot T^{-2}\cdot \theta^{-1}$

NOTE: In 4,

$k$ is the Boltzmann constant, which has a value of

$1.3 \times 10^{-23} J/K$ .