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Q.
Choose the quantity out of the following options that has the same dimensions as Planck’s constant.
NTA AbhyasNTA Abhyas 2020
Solution:
Energy of a photon, $E=h\upsilon$
where h is the Planck’s constant and is the frequency.
$\therefore \left[h\right]=\frac{\left[E\right]}{\left[\upsilon\right]}=\frac{\left[M L^{2} T^{- 2}\right]}{\left[T^{- 1}\right]}=\left[M L^{2} T^{- 1}\right]$
$Angular \, momentum=Moment \, of \, inertia\times Angular \, velocity$
$\left[A n g u l a r \, m o m e n t t u m\right]=\left[M L^{2}\right]\left[T^{- 1}\right]=\left[M L^{2} T^{- 1}\right]$