Q138 / 150 · MHT CET 2020 (13 Oct Shift 1) · Physics

The dimensions of Planck's constant are same as the product of

  • A
    time and displacement.
  • B
    force and time.
  • Correct answer
    C
    force, displacement and time.
  • D
    force and displacement.

Solution

Correct option is $\mathrm{B}$ ) $\mathrm{E}=\mathrm{h} v$ $\Longrightarrow$ Planck's constant $\mathrm{h}=\frac{\mathrm{E}}{\mathrm{v}}$ Dimension of energy $=\left[\mathrm{ML}^{2} \mathrm{~T}^{-2}\right]$ Dimension of $v=\left[\mathrm{T}^{-1}\right]$ Thus dimension of $\mathrm{h}=\left[\mathrm{ML}^{2} \mathrm{~T}^{-1}\right]$ Dimension of Force $=\left[\mathrm{MLT}^{-2}\right]$ Dimension of Displacement=[L] Dimension of Time- $[\mathrm{T}]$ Thus dimension of F orce $\times$ displacement $\times$ time $=\left[\mathrm{ML}^{2} \mathrm{~T}^{-1}\right]=$ Dimension of Planck's constant

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

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