JEE Mains · Physics · STD 11 - 1. units,dimensions and measurement

Given below are two statements : \(Statement\) \((I)\) : Planck's constant and angular momentum have same dimensions. \(Statement\) \((II)\) : Linear momentum and moment of force have same dimensions. In the light of the above statements, choose the correct answer from the options given below :

A Statement \(I\) is true but Statement \(II\) is false
B Both Statement \(I\) and Statement \(II\) are false
C Both Statement \(I\) and Statement \(II\) are true
D Statement \(I\) is false but Statement \(II\) is true

Verified Solution

Answer & Solution

Correct Answer

(A) Statement \(I\) is true but Statement \(II\) is false

Step-by-step Solution

Detailed explanation

\( {[\mathrm{h}]=\mathrm{ML}^2 \mathrm{~T}^{-1}} \) \( {[\mathrm{~L}]=\mathrm{ML}^2 \mathrm{~T}^{-1}} \) \( {[\mathrm{P}]=\mathrm{MLT}^{-1}} \) \( {[\tau]=\mathrm{ML}^2 \mathrm{~T}^{-2}}\) (Here \(\mathrm{h}\) is Planck's constant, \(\mathrm{L}\) is angular momentum,…

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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