MHT CET · Physics · Units and Dimensions
The dimensions of Planck's constant is the same as the product of
- A force and time
- B force, displacement and time
- C force and distance
- D time and displacement
Answer & Solution
Correct Answer
(B) force, displacement and time
Step-by-step Solution
Detailed explanation
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.
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.
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