Q122 / 180 · COMEDK 2019 · Physics

The physical quantity having the same dimensions as Planck's constant $h$ is

  • A
    Boltzmann constant
  • B
    force
  • C
    linear momentumi
  • Correct answer
    D
    angular momentum

Solution

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.

Hence, the correct answer is option: 'D'.

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