Question

The physical quantity that does not have the dimensional formula $\left[M{L}^{-1}{T}^{-2}\right]$ is

• A. force
• B. pressure
• C. stress
• D. modulus of elasticity
• E. energy density

Answer 1

Answer: (A)

$F=mass\times acceleration$

$F=\left[M\right]\left[L{T}^{-2}\right]=\left[ML{T}^{-2}\right]$

$Pressure=Force/Area$

$P=\left[ML{T}^{-2}\right]\left[L^{-2}\right]=\left[M{L}^{-1}{T}^{-2}\right]$

$Stress$ is force per unit area therefore it's dimensional formula will be same as pressure.

$Modulusofelasticity=Fl/A△l=\left[ML{T}^{-2}\right]\left[L\right]\left[L^{-2}\right]\left[L^{-1}\right]=\left[M{L}^{-1}{T}^{-2}\right]$

Hence $D$ is correct answer.