Question:
If A, B and C represent Planck’s constant, mass and velocity respectively, then the dimensional formula of \(\frac{A}{BC}\) is
If A, B and C represent Planck’s constant, mass and velocity respectively, then the dimensional formula of \(\frac{A}{BC}\) is
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Always recall the dimensional formulas of basic quantities:
\begin{itemize}
\item Planck’s constant (h): [ML\textsuperscript{2}T\textsuperscript{-1}]
\item Mass (m): [M]
\item Velocity (v): [LT\textsuperscript{-1}]
\end{itemize}
When dividing physical quantities, subtract the powers of the corresponding base units.
Updated On: Mar 16, 2026
- [M\textsuperscript{0}L\textsuperscript{0}T\textsuperscript{1}]
- [M\textsuperscript{1}L\textsuperscript{0}T\textsuperscript{0}]
- [M\textsuperscript{0}L\textsuperscript{1}T\textsuperscript{0}]
- [M\textsuperscript{1}L\textsuperscript{1}T\textsuperscript{-1}]
Show Solution
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The Correct Option is C
Solution and Explanation
Step 1: Write the dimensional formulas of A, B, and C.
Planck's constant (A): [ML\textsuperscript{2}T\textsuperscript{-1}]
Mass (B): [M]
Velocity (C): [LT\textsuperscript{-1}]
Step 2: Compute the dimensional formula of \(\frac{A}{BC}\).
\[ \frac{A}{BC} = \frac{[ML\textsuperscript{2}T\textsuperscript{-1}]}{[M][LT\textsuperscript{-1}]} = \frac{ML^2T^{-1}}{MLT^{-1}} = L \] So the dimensional formula is: [M\textsuperscript{0}L\textsuperscript{1}T\textsuperscript{0}] Step 3: Select the correct option.
The calculated dimensional formula [M\textsuperscript{0}L\textsuperscript{1}T\textsuperscript{0}] matches option (3).
Planck's constant (A): [ML\textsuperscript{2}T\textsuperscript{-1}]
Mass (B): [M]
Velocity (C): [LT\textsuperscript{-1}]
Step 2: Compute the dimensional formula of \(\frac{A}{BC}\).
\[ \frac{A}{BC} = \frac{[ML\textsuperscript{2}T\textsuperscript{-1}]}{[M][LT\textsuperscript{-1}]} = \frac{ML^2T^{-1}}{MLT^{-1}} = L \] So the dimensional formula is: [M\textsuperscript{0}L\textsuperscript{1}T\textsuperscript{0}] Step 3: Select the correct option.
The calculated dimensional formula [M\textsuperscript{0}L\textsuperscript{1}T\textsuperscript{0}] matches option (3).
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