Answer
Please see the work below.
Work Step by Step
(a) We know that
$L=rmv$
$\implies [L]=[m][Kg][\frac{m}{s}]$
$[L]=kg.\frac{m^2}{s}$
(b) $L=\tau dt$
$L=rFdt$
$[L]=[m][N][s]$
(c) We know that
$K=(\frac{1}{2})I\omega^2=(\frac{1}{2})I(\frac{L}{I})^2$
This simplifies to:
$L=\sqrt{2KI}$
$[L]=\sqrt{[J]}\sqrt{kg.m^2}=kgm^2/s$
