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

The dimensions of Planck's constant are same as the product of
  1. time and displacement.
  2. force and time.
  3. force, displacement and time.
  4. 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

Asked in: MHT CET 2020 (13 Oct Shift 1)

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