Q143 / 150 · MHT CET 2010 · Physics

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

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

Solution

The dimensions of Planck constant, $[h]=\left[\frac{E}{v}\right]=\left[\mathrm{ML}^{2} \mathrm{~T}^{-1}\right]$ Force, $[F]=\left[\mathrm{MLT}^{-2}\right]$ Displacement, $[d]=[\mathrm{L}]$ Time $[t]=[\mathrm{T}]$ $\therefore$ $$ [F][d][t]=\left[\mathrm{MLT}^{-2}\right][\mathrm{L}][\mathrm{T}] $$ $$ =\left[\mathrm{ML}^{2} \mathrm{~T}^{-1}\right] $$ Hence the dimensions of Planck's constant is the same as the product of force, displacement and time.

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

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