The dimensional formula for Planck's constant and angular momentum is:

Question

The dimensional formula for Planck's constant and angular momentum is: (A) [ ML 2 T -2] and [ MLT -1] (B) [ ML 2 T -1] and [ ML 2 T -1] (C) [ ML 2 T 1] and [ ML 2 T -2] (D) [ MLT -1] and [ MLT -2]

Tardigrade Admin · Accepted Answer

Find two relations in which Planck's constant and angular momentum exist and then put dimensions for other physical quantities.
We know that

E = h v

where

h

is Planck's constant,

v

is frequency.

∴ h = \frac{E}{v}

∴ [h] = \frac{[ M L ^{2} T ^{- 2} ]}{[ T ^{- 1} ]} = [M L^{2} T^{- 1}]

Angular momentum

=

momentum

\times

distance

= [M L T^{- 1}] [L]

= [M L^{2} T^{- 1}]

Note : Planck's constant and angular momentum both have the same dimensions.

Q. The dimensional formula for Planck's constant and angular momentum is:

$[M L^{2} T^{- 2}]$ and $[M L T^{- 1}]$

$[M L^{2} T^{- 1}]$ and $[M L^{2} T^{- 1}]$

$[M L^{2} T^{1}]$ and $[M L^{2} T^{- 2}]$

$[M L T^{- 1}]$ and $[M L T^{- 2}]$

Q. The dimensional formula for Planck's constant and angular momentum is:

[ML2T−2] and [MLT−1]

[ML2T−1] and [ML2T−1]

[ML2T1] and [ML2T−2]

[MLT−1] and [MLT−2]

$[M L^{2} T^{- 2}]$ and $[M L T^{- 1}]$

$[M L^{2} T^{- 1}]$ and $[M L^{2} T^{- 1}]$

$[M L^{2} T^{1}]$ and $[M L^{2} T^{- 2}]$

$[M L T^{- 1}]$ and $[M L T^{- 2}]$