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

Dimensions of universal gravitational constant \((G)\) in terms of Planck's constant \((h)\), distance \((L)\), mass \((M)\) and time \((T)\) are _______.

A \([hTLM^{-2}]\)
B \([hT^{-1}LM^{-2}]\)
C \([hTL^2 M^{-2}]\)
D \([h^{-1}T^{-1}LM^{-2}]\)

Verified Solution

Answer & Solution

Correct Answer

(B) \([hT^{-1}LM^{-2}]\)

Step-by-step Solution

Detailed explanation

The dimensional formula of the universal gravitational constant \(G\) is obtained from Newton's law of gravitation \(F = \dfrac{G m_1 m_2}{r^2}\). \([G] = \dfrac{[F][r^2]}{[m_1 m_2]} = \dfrac{[MLT^{-2}][L^2]}{[M^2]} = [M^{-1}L^3T^{-2}]\) The dimensional formula of Planck's…

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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