MHT CET · Physics · Units and Dimensions

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

A time and displacement.
B force and time.
C force, displacement and time.
D force and displacement.

Verified Solution

Answer & Solution

Correct Answer

(C) force, displacement and time.

Step-by-step Solution

Detailed explanation

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

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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