Answer
a) $kg\,m^{2}/s$
b) Units of $\frac{L^{2}}{2mr^{2}}=\frac{(kg\,m^{2}/s)^{2}}{kg\,m^{2}}=kg\,m^{2}s^{-2}= $ units of K.E
Therefore, the expression is dimensionally correct.
c) $kg\,m^{2}$
Work Step by Step
a) Units of L= unit of mass$\times$ units of speed$\times$ unit of radius
= $kg\times ms^{-1}\times m=kg\,m^{2}/s$
b) Units of L= $kg\,m^{2}/s$
Units of $mr^{2}= kg\,m^{2}$
Units of $\frac{L^{2}}{2mr^{2}}=\frac{(kg\,m^{2}/s)^{2}}{kg\,m^{2}}=kg\,m^{2}s^{-2}= $ units of K.E
Therefore, the expression is dimensionally correct.
c) Units of moment of inertia= $unit\,of\,mass\times(unit\,of\,r)^{2}= kg\,m^{2}$
