Question

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

• A. $\left[ ML ^{2} T ^{-2}\right]$ and $\left[ MLT ^{-1}\right]$
• B. $\left[ ML ^{2} T ^{-1}\right]$ and $\left[ ML ^{2} T ^{-1}\right]$
• C. $\left[ ML ^{2} T ^{1}\right]$ and $\left[ ML ^{2} T ^{-2}\right]$
• D. $\left[ MLT ^{-1}\right]$ and $\left[ MLT ^{-2}\right]$

Answer 1

Answer: (B)

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.
$\therefore h=\frac{E}{v}$
$\therefore [h]=\frac{\left[ ML ^{2} T ^{-2}\right]}{\left[ T ^{-1}\right]}=\left[ ML ^{2} T ^{-1}\right]$
Angular momentum $=$ momentum $\times$ distance
$=\left[ MLT ^{-1}\right][ L ] $
$=\left[ ML ^{2} T ^{-1}\right]$
Note : Planck's constant and angular momentum both have the same dimensions.