The dimensions of Planck's constant and angul | vedclass

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Question

(B) Planck's constant $(h)$ is related to energy $(E)$ and frequency $(f)$ by the equation $E = hf$. Therefore,$h = E/f$. The dimension of energy is $

Vedclass · Accepted Answer

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

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(B) Planck's constant $(h)$ is related to energy $(E)$ and frequency $(f)$ by the equation $E = hf$. Therefore,$h = E/f$. The dimension of energy is $[M L^2 T^{-2}]$ and the dimension of frequency is $[T^{-1}]$. Thus,the dimension of $h$ is $[M L^2 T^{-2}] / [T^{-1}] = [M L^2 T^{-1}]$.Angular momentum $(L)$ is given by the formula $L = mvr$,where $m$ is mass,$v$ is velocity,and $r$ is radius. The dimensions are $[M] [L T^{-1}] [L] = [M L^2 T^{-1}]$.Since both quantities have the same dimensions $[M L^2 T^{-1}]$,the correct option is $B$.

The dimensions of Planck's constant and angular momentum are respectively:

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