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EEJ MAIN Physics QUESTION #7084
Question 1
If velocity ($V$), acceleration ($A$), and force ($F$) are the fundamental units, find the dimensions of Young's modulus.
  • $V^{-2}A^{2}F^{-2}$
  • $V^{-2}A^{2}F^{2}$
  • $V^{-4}A^{-2}F$
  • $V^{-4}A^{2}F$✔️
Correct Answer Explanation

Young's Modulus $[Y] = [ML^{-1}T^{-2}]$.

  • Force $[F] = [MLT^{-2}] \implies M = F L^{-1} T^2$
  • Velocity $[V] = [LT^{-1}]$ and Acceleration $[A] = [LT^{-2}]$
  • Solving for $L$ and $T$: $T = V/A$ and $L = V^2/A$.
  • Substituting these into the formula for $Y$ yields $V^{-4}A^2F$.