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  4. Plancks constant has same dimension as:

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Q. Plancks constant has same dimension as:

Rajasthan PMTRajasthan PMT 2005Physical World, Units and Measurements

Solution:

The dimension of Planck's constant is given by
$h=\frac{E}{v} =\frac{\left[M L^{2} T^{-2}\right]}{\left[T^{-1}\right]}$
$=\left[M L^{2} T^{-1}\right]$
Dimension of angular momentum is $=$ moment of inertia $\times$ angular velocity $=\left[ ML ^{2}\right]\left[ T ^{-1}\right]=\left[ ML ^{2} T ^{-1}\right]$
So, the dimension of Planck's constant is same as of angular momentum.