Question

If A, B and C represent Planck’s constant, mass and velocity respectively, then the dimensional formula of \(\frac{A}{BC}\) is

• A. [M\textsuperscript{0}L\textsuperscript{0}T\textsuperscript{1}]
• B. [M\textsuperscript{1}L\textsuperscript{0}T\textsuperscript{0}]
• C. [M\textsuperscript{0}L\textsuperscript{1}T\textsuperscript{0}]
• D. [M\textsuperscript{1}L\textsuperscript{1}T\textsuperscript{-1}]

Hint:

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.

Answer 1

The Correct Option is C

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).