The ratio of the dimensions of plank's constant and that of the moment of inertia is the dimension of

Options

A. frequency
B. velocity
C. angular momentum
D. time

Answer

A

Explanation

Energy carried by photon is given by
`E = hv`
`rArr h =` Plancks's constant `= (E)/(v)`
`:. [h] = ([ML^(2)T^(-2)])/([T^(-1)] = [ML^(2)T^(-1)]`
and `I =` moment of inertia `= MR^(2)`
`rArr [I] = [ML^(2)]`
Hence, `([h])/([I]) = ([ML^(2)T^(-1)])/([ML^(2)]) = [T^(-1)]`
`= (1)/([T]) =` dimension of frequency
Alternative
`(h)/(I) = (E//v)/(I)`
`= (E xx T)/(I) = ((kg-m^(2)//s^(2))xx s)/((kg-m^(2)))`
`= (1)/(s) = (1)/("time") =` frequency
Thus, dimensions of `(h)/(I)` is same as that of frequency.