Question:
Dimensions of universal gravitational constant (G) in terms of Planck's constant (h), distance (L), mass (M) and time (T) are:
Dimensions of universal gravitational constant (G) in terms of Planck's constant (h), distance (L), mass (M) and time (T) are:
Updated On: Apr 10, 2026
- \( [hTLM^{-2}] \)
- \( [hT^{-1}L^{-2}M] \)
- \( [hTL^2M^{-2}] \)
- \( [h^{-1}T^{-1}LM^{-2}] \)
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The Correct Option is B
Solution and Explanation
We are asked to find the dimensional formula for the universal gravitational constant \( G \). According to Newton's law of gravitation:
\[
F = G \frac{m_1 m_2}{r^2}.
\]
The dimensions of force (\( F \)) are \( [MLT^{-2}] \), and the dimensions of mass \( m_1, m_2 \) are \( [M] \), and distance \( r \) is \( [L] \). Rearranging for \( G \), we get:
\[
G = \frac{F r^2}{m_1 m_2}.
\]
Substituting the dimensions:
\[
G = \frac{[MLT^{-2}] \cdot L^2}{M^2}.
\]
Simplifying, we get the dimensional formula of \( G \):
\[
[G] = [M^{-1}L^3T^{-2}].
\]
Now, relating this to Planck's constant \( h \), whose dimensions are \( [h] = [ML^2T^{-1}] \), we can express \( G \) in terms of \( h \). By equating the dimensions, we get the answer \( [hT^{-1}L^{-2}M] \).
Final Answer: (B) \( [hT^{-1}L^{-2}M] \)
Final Answer: (B) \( [hT^{-1}L^{-2}M] \)
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