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The physical quantity having the same dimensions as Planck's constant $h$ is
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Verified Answer
The correct answer is:
angular momentum
Dimensional formula of Planck's constant $=\left[\mathrm{M}^{1} \mathrm{~L}^{2} \mathrm{~T}^{-1}\right]$
Similarly,
Boltzmann constant is given
$$
K=\frac{\text { Energy }}{\text { Temperature }}
$$
$\therefore$ The dimension of $K$ is
$$
=\frac{\left[M L^{2} T^{-2}\right]}{[K]}=\left[M^{1} L^{2} T^{-2} K^{-1}\right]
$$
Dimensional formula of force is $\left[\mathrm{M}^{\mathrm{l}} \mathrm{L}^{1} \mathrm{~T}^{-2}\right]$.
Dimensional formula of linear momentum is $\left[M^{1} L^{1} T^{-1}\right]$.
Dimensional formula of angular momentum is $\left[\mathrm{M}^{1} \mathrm{~L}^{2} \mathrm{~T}^{-1}\right]$.
Hence, angular momentum and Planck's constant have same dimensional formula.
Similarly,
Boltzmann constant is given
$$
K=\frac{\text { Energy }}{\text { Temperature }}
$$
$\therefore$ The dimension of $K$ is
$$
=\frac{\left[M L^{2} T^{-2}\right]}{[K]}=\left[M^{1} L^{2} T^{-2} K^{-1}\right]
$$
Dimensional formula of force is $\left[\mathrm{M}^{\mathrm{l}} \mathrm{L}^{1} \mathrm{~T}^{-2}\right]$.
Dimensional formula of linear momentum is $\left[M^{1} L^{1} T^{-1}\right]$.
Dimensional formula of angular momentum is $\left[\mathrm{M}^{1} \mathrm{~L}^{2} \mathrm{~T}^{-1}\right]$.
Hence, angular momentum and Planck's constant have same dimensional formula.
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