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

The ratio of the dimensions of Planck's constant and that of the moment of inertia is the dimensions of
  1. time
  2. frequency
  3. angular momentum
  4. velocity

Solution

$\frac{\text { Planck's constant }}{\text { Moment of inertia }}=\frac{\frac{2 \pi \mathrm{I} \omega}{\mathrm{n}}}{\mathrm{I}}$
[As $\left.\frac{\mathrm{nh}}{2 \pi}=\mathrm{I} \omega\right]$
$
=\frac{2 \pi \mathrm{I}(2 \pi \mathrm{f})}{\mathrm{nI}}=\left(\frac{4 \pi^{2}}{\mathrm{n}} \cdot \mathrm{f}\right)=\left[\mathrm{T}^{-1}\right]
$

Asked in: JEE Mains - Units and Dimensions - Test 3

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